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JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 8 - MCQExams.com
JEE
Maths
Straight Line And Pair Of Straight Lines
Quiz 8
If (–2,is the image of the point (4,with respect to line L = 0, then L =
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3x – 2y + 5
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3x – 2y + 10
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2x + 3y – 5
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6x – 4y – 7
The point P is the intersection of the straight line joining the points Q(2,3,and P(1,–1,with the plane 5x – 4y – z = 1. If S is the foot of the perpendicular drawn from the point T(2,1,to QR, then the length of the line segment PS is
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2)
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2
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2)
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None of these
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2)
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0
Explanation
It is obvious
The triangle formed by the lines x + y – 4 = 0, 3x + y = 4, x + 3y = 4 is
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Isoscles
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Equilateral
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Right angled
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None of these
The area of a parallelogram formed by the lines ax ± by ± c = 0, is
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2)
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None of these
A point moves so that square of its distance from the point (3,-is numerically equal to its distance from the line 5x – 12y = 13. The equation of the locus of the point is
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13x2 + 13y2 – 83x + 64y + 182 = 0
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x2 + y2 – 11x + 16y + 26 = 0
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x2 + y2 – 11x + 16y = 0
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None of these
Locus of the points which are at equal distance from 3x + 4y – 11 = 0 and 12x + 5y + 2 = 0 and which is near the origin is
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21x – 77y + 153 = 0
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99x + 77y – 133 = 0
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7x – 11y = 19
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None of these
A point moves such that its distance from the point (4,is half that of its distance from the line x = 16. The locus of this point is
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3x2 + 4y2 = 192
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4x2 + 3y2 = 192
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x2 + y2 = 192
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None of these
If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
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Square
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Circle
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Straight line
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Two intersecting lines
The point moves such that the area of the triangle formed by it with points (1,and (3,–is 21 sq.unit. The locus of the point is
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6x + y – 32 = 0
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6x – y + 32 = 0
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x + 6y – 32 = 0
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6x – y – 32 = 0
A straight line through the point, (1,meets the x-axis at \'A\' and the y-axis at \'B\' . The locus of the mid-point of AB is
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2xy + x + y = 0
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x + y – 2xy = 0
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x + y + 2 = 0
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x + y – 2 = 0
The points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10,are
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(3, 1), (–7, 11)
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(3, 1), (7, 11)
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(–3, 1), (–7, 11)
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(1, 3), (–7, 11)
If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are a and b be p, then
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2)
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The perpendicular distance of the straight line 12x + 5y = 7 from the origin is given by
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2)
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The distance between 4x + 3y = 11 and 8x + 6y = 15, is
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4
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None of these
A line passes through the point of intersection of the lines 3x + y + 1 = 0 and 2x – y + 3 = 0 and makes equal intercepts with axes. Then equation of the line is
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5x + 5y – 3 = 0
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x + 5y – 3 = 0
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5x – y – 3 = 0
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5x + 5y + 3 = 0
If the line y = 7x – 25 meets the circle x
2
+ y
2
= 25 in the points A, B, then the distance between A and B is
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0%
10
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5
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(4,7)
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(7,4)
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(5,7)
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(–5, –3)
The distance of the point (–2,from the line x – y = 5 is
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2)
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The distance of the lines 2x – 3y = 4 from the point (1,measured parallel to the line x + y = 1 is
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2)
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6
The length of the straight line x – 3y = 1 intercepted by the hyperbola x
2
– 4y
2
= 1, is
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2)
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Distance between the parallel lines 3x + 4y + 7 = 0 and 3x + 4y – 5 = 0 is
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2)
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The equation of straight line equally inclined to the axis and equidistant from the points (1, –and (3,is ax + by + c = 0 where
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a = 1, b = 1, c = 1
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a = 1, b = –1, c = –1
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a = 1, b = 1, c = 2
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None of these
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0%
2)
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The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at (4, –is
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3x + 4y = 24
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3x – 4y = 12
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3x – 4y = 24
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4x – 3y = 24
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4x – 3y = 12
The length of perpendicular from a point (1,to the straight line 3x + 4y + 4 = 0
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5
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3
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7/5
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None of these
Two lines represented by equations x + y = 1 and x + ky = 0 are mutually orthogonal if k is
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1
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–1
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0
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None of these
The equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, –1). The length of the side of the triangle is
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2)
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None of these
(sin θ, cos θ) and (3,lies on the same side of the line x + y = 1, then θ lies between
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2)
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Let α be the distance between the lines –x + y = 2 and x – y = 2, and β be the distance between the lines 4x – 3y = 5 and 6y – 8x = 1, then
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0%
2)
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None of these
Choose the correct statement which describe the position of the point (–6,relative to straight lines 2x + 3y – 4 = 0 and 6x + 9y + 8 + 0
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Below both the lines
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Above both the lines
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In between the lines
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None of the above
The position of the points (3,and (2, –with respect to the line 3x – 4y = 8 are
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On the same side of the line
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On different side of the line
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One point on the line and the other outside the line
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Both points on the line
A ray of light coming from the point (1,is reflected at a point A on the
x
-axis and then passes through the point (5,3). The coordinates of the point A are
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0%
2)
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None of these
If the co-ordinates of the middle point of the portion of a line intercepted between coordinates axes is (3,2), then the equation of the line will be
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2x + 3y = 12
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3x + 2y = 12
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4x – 3y = 6
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5x – 2y = 10
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2x + 3y + 22 = 0
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5x – 4y + 7 = 0
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3x – 2y + 3 = 0
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None of these
The equation of perpendicular bisectors of the sides AB and AC of a triangle ABC are x – y + 5 = 0 and x + 2y = 0 respectively. If the point A is (1, –2), then the equation of line BC is
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23x + 14y – 40 = 0
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14x – 23y + 40 = 0
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23x – 14y + 40 = 0
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14x + 23y – 40 = 0
The medians AD and BE of a triangle with vertices A(0,b), B(0,and C(a,are perpendicular to each other, if
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2)
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Both (a) and (b)
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None of these
Let PS be the median of the triangle with vertices P(2,2), Q(6, –and R(7, 3). The equation of the line passing through (1, –and parallel to PS is
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2x – 9y – 7 = 0
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2x – 9y – 11 = 0
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2x + 9y – 11 = 0
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2x + 9y + 7 = 0
The equation of straight line passing through (–a,and making the triangle with axes of area \'T\' is
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2Tx + a2y + 2aT = 0
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2Tx – a2y + 2aT = 0
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2Tx – a2y – 2aT = 0
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None of these
If the equation of base of an equilateral triangle is 2x – y = 1 and the vertex is (–1,2), then the length of the side of the triangle is
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0%
2)
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1f x
1
, x
2
, x
3
and y
1
, y
2
, y
3
are both in G.P. with the same common ratio, then the points (x
1
, y
1
) , (x
2
, y
2
) and (x
3
, y
3
)
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Lie on a straight line
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Lie on an ellipse
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Lie on a circle
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Are vertices of a triangle
A line 4x + y = 1 passes through the point A(2, –meets the lines BC whose equation is 3x – 4y + 1 = 0 at the point B. The equation of the line AC so that AB = AC, is
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52x + 89y + 519 = 0
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52x + 89y – 519 = 0
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89x + 52y + 519 = 0
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89x + 52y – 519 = 0
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30o
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45o
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60o
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75o
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1
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2
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3
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4
Given vertices A(1,1), B(4, –and C(5,of a triangle, then the equation of the perpendicular dropped from C to the interior bisector of the angle A is
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y – 5 = 0
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x – 5 = 0
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y + 5 = 0
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x + 5 = 0
The vertices of a triangle are (2,1), (5,and (4,4). The lengths of the perpendicular from these vertices on the opposite sides are
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2)
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0%
Given the four lines with equations x + 2y = 3, 3x + 4y = 7, 2x + 3y = 4 and 4x + 5y = 6, then these lines are
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Concurrent
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Perpendicular
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The sides of a rectangle
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None of these
The line 3x + 2y = 24 meets y-axis at A and x-axis at B. The perpendicular bisector of AB meets the line through (0, –parallel to x-axis at C. The area of the triangle ABC is
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182 sq.units
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91 sq.units
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48 sq.units
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None of these
A pair of straight lines drawn through the origin form with the line 2x + 3y = 6 an isosceles right angled triangle, then the lines and the area of the triangle thus formed is
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0%
2)
0%
0%
None of these
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