JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 12

One diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is (1,2). Then the equation of the sides of the square passing through this vertex, are

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23x + 7y = 9, 7x + 23y = 53
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23x – 7y + 9 = 0, 7x + 23y + 53 = 0
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23x – 7y – 9 = 0, 7x + 23y – 53 = 0
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None of the above

Maths-Straight Line and Pair of Straight Lines-52339.png

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None of these

The equation of the line which makes right angled triangle with axes whose area is 6 sq. units and whose hypothenuse it of 5 units, is

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A(–1,1), B(5,are opposite vertices of a square in xy-plane. The equation of the other diagonal [not passing through (A.B)] of the square is given by

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x – 3y + 4 = 0
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2x – y + 3 = 0
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y + 3x – 8 = 0
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x + 2y – 1 = 0

Equations of diagonals of square formed by lines x = 0, y = 0, x = 1 and y = 1 are

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y = x, y + x = 1
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y = x, x + y = 2
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2y = x, y + x = 1/3
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y = 2x, y + 2x = 1

Maths-Straight Line and Pair of Straight Lines-52351.png

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None of these

Maths-Straight Line and Pair of Straight Lines-52356.png

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Maths-Straight Line and Pair of Straight Lines-52362.png

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The same straight line u
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Different straight line
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It is not a straight line
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None of the above

For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in the length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes ?

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Maths-Straight Line and Pair of Straight Lines-52369.png

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All of the above

The equations (b – c)x + (c – a)y + (a – b) = 0 and (b³ – c³)x + (c³ – a³)y + a³ – b³ = 0 will represent the same line, if

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b = c
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c = a
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a = b
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a + b + c = 0
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All of these

The triangle PQR is inscribed in the circle x² + y² = 25. If Q and R have co-ordinates (3,and (–4,respectively, then ∠QPR is equal to

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Equation of the straight line making equal intercepts on the axes and passing through the point (2,is

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4x – y – 4 = 0
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2x + y – 8 = 0
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x + y – 6 = 0
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x + 2y – 10 = 0

The equations of the straight line passing through the point (4,and making intercepts on the co-ordinate axes whose sum is –1 are

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Maths-Straight Line and Pair of Straight Lines-52386.png

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Maths-Straight Line and Pair of Straight Lines-52392.png

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–2
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–1
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2
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1
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0

The equation of the perpendicular bisector of the line segment joining A(–2,and B(6, –is

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x – y = –1
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x – y = 3
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x + y = 3
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x + y = 1
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x + y = –1

If the three points A(1,6), B(3, –and C(x, y) are colinear, then the equation satisfying by x and y is

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5x + y – 11 = 0
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5x + 13y + 5 = 0
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5x – 13y + 5 = 0
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13x – 5y +5 = 0

The equation of one of the lines parallel to 4x – 3y = 5 and at a unit distance from the point (–1, –is

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3x + 4y – 3 = 0
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3x + 4y + 3 = 0
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4x – 3y + 3 = 0
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4x – 3y – 3 = 0
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4x – 3y – 4 = 0

A person standing at the junction (crossing) of two straight paths represented by the equations x + y + 1 = 0 and x – y + 1 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in least time.The equation of the path that he should follow is

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7x + 6y + 7 = 0
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6x + 7y + 7 = 0
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7x + 6y + 4 = 0
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6x + 7y + 4 = 0

If a, b, c are in A.P. and x, y, z are in G.P., then the points (a, x), (b, y) and (c, z) are collinear if

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x2 = y
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x = z2
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y2 = z
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x = y = z

Maths-Straight Line and Pair of Straight Lines-52399.png

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0
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none of these

Maths-Straight Line and Pair of Straight Lines-52403.png

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Through the point (13,a st. line is drawn to meet the axes of x and y at Q and S respectively. If the rectangle OQRS is completed, the co–ordinates of R satisfy the equation.

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If the vertices A and B of a triangle ABC are given by (2,and (4, –and C moves along the line L₁ : 9x + 7y + 4= 0, the locus of the centroid of the triangle ABC is a st. line parallel to

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AB
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BC
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CA
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L1

The vertex O of an isosceles triangle OAB lies at the origin and the equation of the base AB is x – y + 1 = 0. If OA = OB = 6, the area of the triangle OAB is

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Maths-Straight Line and Pair of Straight Lines-52420.png

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A.P.
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G.P.
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H.P.
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none of these

Given the points A (0, a) and B (0, – a), the equation of the locus of point P (x, y) such that |AP – BP| = 6 is

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The points A (0, 0), B (cosα , sinα ) and C (cosβ, sinβ) are the vertices of a right angled triangle if

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none of these

A line 2x + 3y – 1 = 0 intersects the three sides BC, CA, and AB of the triangle ABC in P, Q, R respectively. Then

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If m₁, m₂ are the roots of the equation x² – ax – a – 1 = 0, then the area of the triangle formed by the three st. lines y = m₁x, y=m₂x and y = a(a ≠ –is

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none of these

If the area of the triangle whose vertices are (b, c), (c, a) and (a , b) is ∆, then the area of the triangle whose vertices are (ac – b², ab – c²), (ba – c², bc – a²), and (cb – a², ca – b²) is

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(a + b + c)∆
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(a + b + c)2∆
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2(a + b + c)∆
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none of these

Two vertices of a triangle are (5, –and (–2, 3). If the orthocentre of the triangle is at (0, 0), then the third vertex is

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(4, 7)
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(7, 4)
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(–4, –7)
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(–7, –4)

If (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the co–ordinates of the circumcentre, the centroid and the orthocentre of a triangle, then

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3x1 = 2x2 +x1; 3y1 = 2y 2 + y3
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3x2 = 2x1 + x3; 3y2 = 2y 1 + y3
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3x3 = 21 + x2; 3y3 = 2y1 + y2
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x1 = x2 = x3; y1 = y2 = y3

Maths-Straight Line and Pair of Straight Lines-52443.png

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Maths-Straight Line and Pair of Straight Lines-52449.png

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Maths-Straight Line and Pair of Straight Lines-52455.png

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Maths-Straight Line and Pair of Straight Lines-52460.png

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None of these

Maths-Straight Line and Pair of Straight Lines-52465.png

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Maths-Straight Line and Pair of Straight Lines-52470.png

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None of these

Maths-Straight Line and Pair of Straight Lines-52475.png

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None of these

Maths-Straight Line and Pair of Straight Lines-52480.png

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None of these

The line 2x + 3y = 12 meets the x-axis at A and y-axis at B. The line through (5,perpendicular to AB meets the x-axis, y-axis and the given line at C,D and E respectively. If O is the origin of coordinates, then the area of OCEB is

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23 sq. units
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None of these

The pedal points of a perpendicular drawn from origin on the line 3x + 4y – 5 = 0, is

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Maths-Straight Line and Pair of Straight Lines-52492.png

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Maths-Straight Line and Pair of Straight Lines-52498.png

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None of these

If A is (2, 5), B is (4, –and C lies on 9x + 7y + 4 = 0, then the locus of the centroid of the ∆ABC is a straight line parallel to the straight line is