In the equation y – y 1 =m(x – x 1 ) if m and x 1 are fixed and different lines are drawn form different value of y 1 , then

There will be a set of parallel lines

The lines will pass through a single point

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 9

Maths-Straight Line and Pair of Straight Lines-52009.png

0%
ab
0%
2)
0%
2ab
0%

Maths-Straight Line and Pair of Straight Lines-52013.png

0%
0%
2)
0%
0%

The three lines px + qy + r = 0, qx + ry + p = 0, rx + py + q = 0 are concurrent if

0%
p + q + r = 0
0%
p2 + q2 + r2 = pq + qr + pr
0%
p3 + q3 + r3 = 3pqr
0%
None of these
0%
All (1), (and (3)

The line joining two points A(2,0), B(3,is rotated about A in anti-clockwise direction through an angle of 15^o. The equation of the line in the new position , is

0%
0%
2)
0%
0%

In the equation y – y₁ =m(x – x₁ ) if m and x₁ are fixed and different lines are drawn form different value of y₁ , then

0%
The lines will pass through a single point
0%
There will be a set of parallel lines
0%
There will be one line only
0%
None of these

The straight line passing through the point of intersection of the straight lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and having infinite Slope and at a distance of 2 units from the origin, has the equation

0%
x = 2
0%
3x + y – 1= 0
0%
y = 1
0%
None of these

For the straight lines given by the equation (2 + k)x + (1 + k)y = 5 + 7k, for different values of k which of the following statements is true

0%
Lines are parallel
0%
Lines pass through the point (–2, 9)
0%
Lines pass through the point (2, –9)
0%
None of these

Co-ordinates of the vertices of a quadrilateral are (2, –1), (0, 2), (2,and (4, 0). The angle between its diagonals will be

0%
90o
0%
0o
0%
tan-1(2)
0%

Equation of one of the sides of an isosceles right-angled triangle whose hypotenuse is 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2,2), will be

0%
x – 7y + 12 = 0
0%
7x + y – 12 = 0
0%
x – 7y + 16 = 0
0%
7x + y + 16 = 0

The diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n\' = 0, mx + ly + n = 0, mx + ly + n\' = 0 include an angle

0%
0%
2)
0%
0%

The equation of bisectors of the angles between the lines |x| = |y| are

0%
y = ± x and x = 0
0%
2)
0%
y = 0 and x = 0
0%
None of these

The area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

0%
0%
2)
0%
0%

A point starts moving from (1,and its projection on x and y-axis are moving with velocities of 3m/s and 2m/s respectively. Its locus is

0%
2x – 3y + 4 = 0
0%
3x – 2y + 1 = 0
0%
3y – 2x + 4 = 0
0%
2y – 3x + 1 = 0

Maths-Straight Line and Pair of Straight Lines-52042.png

0%
0%
2)
0%
0%

The lines p(p² +x – y + q = 0 and (p² + 1)² x + (p² + 1)y + 2q = 0 are perpendicular to a common line for

0%
No value of p
0%
Exactly one value of p
0%
Exactly two values of p
0%
More than two values of p

The equation of the locus of the point of intersection of the straight lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ)y + a sin θ = 0 is

0%
y = ± ax
0%
x = ± ay
0%
y2 = 4ax
0%
x2 + y2 = a2

If P is a point (x,y) on the line y = –3x such that P and the point (3,are on the opposite sides of the line 3x – 4y – 8 = 0, then

0%
0%
2)
0%
0%
None of these

If the equations of opposite sides of a parallelogram are x² – 7x + 6 = 0 and y² – 14y + 40 = 0, then the equation of its one diagonal is

0%
6x + 5y + 14 = 0
0%
6x – 5y + 14 = 0
0%
5x + 6y + 14 = 0
0%
5x – 6y + 14 = 0

The image of the pair of lines represented by ax² + 2hxy + by² = 0 by the line mirror y = 0 is

0%
ax2 – 2hxy – by2 = 0
0%
bx2 – 2hxy – ay2 = 0
0%
bx2 + 2hxy + ay2 = 0
0%
ax2 – 2hxy + by2 = 0

If the portion of the line lx + my = 1 falling inside the circle x² + y² = a² subtends an angle of 450 at the origin, then

0%
0%
2)
0%
0%
None of these

If the pair of lines ax² + 2hxy + by² + 2gx + 2fy + c = 0 intersect on the y-axis, then

0%
2fgh = bg2 + ch2
0%
bg2 ≠ ch2
0%
abc = 2fgh
0%
None of these

Maths-Straight Line and Pair of Straight Lines-52061.png

0%
1
0%
2)
0%
0
0%

The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a,b) is

0%
x2 + y2 – ax – by = 0
0%
x2 + y2 + ax + by = 0
0%
x2 + y2 – 2ax – 2by = 0
0%
None of these

The equations to a pair of opposite sides of a parallelogram are x² – 5x + 6 = 0 and y² – 6y + 5 = 0. The equations to its diagonals are

0%
x + 4y = 13 and y = 4x – 7
0%
4x + y = 13 and 4y = x – 7
0%
4x + y = 13 and y = 4x – 7
0%
y – 4x = 13 and y + 4x = 7

Area of the triangle formed by the lines y² – 9xy + 18x² = 0 and y = 9 is

0%
0%
27 sq. units
0%
0%
None of these

The area (in square units) of the quadrilateral formed by the two pairs of lines
l² x² – m² y² – n(lx + my) = 0 and
l² x² – m² y² + n(lx – my) = 0 is

0%
0%
2)
0%
0%

Maths-Straight Line and Pair of Straight Lines-52075.png

0%
Straight line
0%
Pair of straight lines
0%
Circle
0%
Ellipse

The equation of the pair of straight lines, each of which makes an angle α with the line y = x, is

0%
x2 + 2xy sec 2α + y2 = 0
0%
x2 + 2xy cosec 2α + y2 = 0
0%
x2 – 2xy cosec 2α + y2 = 0
0%
x2 – 2xy sec 2α + y2 = 0

Maths-Straight Line and Pair of Straight Lines-52078.png

0%
0%
2)
0%
0%
None of these

The figure formed by the lines x² + 4xy + y² = 0 and x – y = 4 is

0%
A right-angled triangle
0%
An isosceles triangle
0%
An equilateral triangle
0%
None of these

If one of the lines of the pair ax² + 2hxy + by² = 0 bisects the angle between positive directions of the axes, then a,b,h satisfy the relation

0%
a + b = 2|h|
0%
a + b = –2h
0%
a – b = 2|h|
0%
(a – b)2 = 4h2

The lines joining the origin to the points of intersection of the line y = mx + c and the circle x² + y² = a² will be mutually perpendicular, if

0%
a2 (m2 += c2
0%
a2 (m2 –= c2
0%
a2 (m2 += 2c2
0%
a2 (m2 –= 2c2

The angle between the lines joining the points of intersection of line y = 3x + 2 and the curve x² + 2xy + 3y² + 4x + 8y – 11 = 0 to the origin, is

0%
0%
2)
0%
0%

If the lines ax² + 2hxy + by² = 0 represent the adjacent sides of a parallelogram, then the equation of second diagonal if one is lx + my = 1, will be

0%
(am + hl)x = (bl + hm)y
0%
(am – hl)x = (bl – hm)y
0%
(am – hl)x = (bl + hm)y
0%
None of these

If the pair of lines ax² + 2(a + b) xy + by² = 0 lies along diameters of a circle and divides the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then

0%
3a2 + 10 ab + 3b2 = 0
0%
3a2 + 2 ab + 3b2 = 0
0%
3a2 – 10 ab + 3b2 = 0
0%
3a2 – 2 ab + 3b2 = 0

The equation of the pair of straight lines parallel to x-axis and touching the circle x² + y² – 6x – 4y – 12 = 0

0%
y2 – 4y – 21 = 0
0%
y2 + 4y – 21 = 0
0%
y2 – 4y + 21 = 0
0%
y2 + 4y + 21 = 0

Maths-Straight Line and Pair of Straight Lines-52094.png

0%
0%
2)
0%
0%

The lines represented by the equation ax² + 2hxy + by² + 2gx + 2fy + c = 0 will be equidistant from the origin, if

0%
f 2 + g2 = c(b – a)
0%
f 4 + g4 = c(bf 2 + ag2)
0%
f 4 – g4 = c(bf 2 – ag2)
0%
f 2 + g2 = af 2 + bg2

The area enclosed by the pair of lines xy = 0, the line x – 4 = 0 and y + 5 = 0 is

0%
20 sq.units
0%
10 sq.units
0%
5/4 sq.units
0%
0 sq.units

The graph of y = |x| consists of a pair of straight lines lying

0%
To the left of y-axis
0%
Above x-axis
0%
Below x-axis
0%
To the right of y-axis

Maths-Straight Line and Pair of Straight Lines-52103.png

0%
0%
2)
0%
0%

Distance between two lines represented by the pair of straight lines x² – 6xy + 9y² + 3x – 9y – 4 = 0 is

0%
0%
2)
0%
0%

If the lines joining origin to the points of intersection of the line fx – gy = λ and the curve x² + hxy – y² + gx + fy = 0 be mutually perpendicular, then

0%
λ = h
0%
λ = g
0%
λ = fg
0%
λ may have any value

The equation of the line joining origin to the points of intersection of the curve x² + y² = a² and x² + y² – ax – ay = 0 is

0%
x2 – y2 = 0
0%
xy = 0
0%
xy – x2 = 0
0%
y2 + xy = 0

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve x² + y² = 4 with x + y = a. The set containing the value of \'a\' is

0%
{–2, 2}
0%
{–3, 3}
0%
{–4, 4}
0%
{–5, 5}

The equation of pair of straight lines joining the point of intersection of the curve x² + y² = 4 and y – x = 2 to the origin, is

0%
x2 + y2 = (y – x)2
0%
x2 + y2 + (y – x)2 = 0
0%
x2 + y2 = 4(y – x)2
0%
x2 + y 2 + 4(y – x)2 = 0

The lines joining the points of intersection of line x + y = 1 and curve x² + y² – 2y + λ = 0 to the origin are perpendicular, then the value of λ will be

0%
0%
2)
0%
0%
0

The lines joining the points of intersection of the curve (x – h)² + (y – k)² – c² = 0 and the line kx + hy = 2hk to the origin area perpendicular, then

0%
c = h ± k
0%
c2 = h2 + k2
0%
c2 = (h + k)2
0%
4c2 = h2 + k2

If the distance of two lines passing through origin from the point (x₁, y₁) is \'d\' , then the equation of lines is

0%
0%
2)
0%
0%

The lines joining the origin to the points of intersection of the line 3x – 2y = 1 and the curve 3x² + 5xy – 3y² + 2x + 3y = 0, are

0%
Parallel to each other
0%
Perpendicular to each other
0%
Inclined at 45o to each other
0%
None of these

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 9 - MCQExams.com

0:0:1

Practice Maths Quiz Questions and Answers

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 9 - MCQExams.com

0:0:1

Practice Maths Quiz Questions and Answers

Support mcqexams.com by disabling your adblocker.