Straight Line and Pair of Straight Lines Test

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Straight Line and Pair of Straight Lines Test - 51

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Question 1
4 / -1

Separate equations of lines, for a pair of lines, whose equation is x² + xy – 12y² = 0 are

A
x + 4y = 0 and x + 3y = 0

B
2x – 3y = 0 and x – 4y = 0

C
x – 6y = 0 and x – 3y = 0

D
x + 4y = 0 and x – 3y = 0
Question 2
4 / -1

The equation of the lines represented by the equation ab (x² – y²) + (a² – b²) xy = 0 are

A
ax – by = 0, bx + ay = 0

B
ax – by = 0, bx – ay = 0

C
ax + by = 0, bx + ay = 0

D
ax + by = 0, bx – ay = 0

Solution
Question 3
4 / -1

The straight line 3x + 4y – 5 = 0 and 4x = 3y + 15 intersect at the point P. On these lines the points Q and R are chosen so that PQ = PR. The slopes of the lines QR passing through (1,2) are

A

B

C

D

Solution
Question 4
4 / -1

The lines represented by the equation ax² (b – c) – xy(ab – bc) + cy² (a – b) = 0, are

A
a(b – c)x – c(a – b)y = 0, x + y = 0

B
x + y = 0, x – y = 0

C
a(b – c) x – c (a – b)y = 0, x – y = 0

D
None of these
Question 5
4 / -1

The nature of straight lines represented by the equation 4x² + 12xy + 9y² = 0, is

A
Real and coincident

B
Real and different

C
Imaginary and different

D
None of the above

Solution
Question 6
4 / -1

The equation of the perpendiculars drawn from the origin to the lines represented by the equation 2x² – 10xy + 12y² + 5x – 16y – 3 = 0 is

A
6x² + 5xy + y² = 0

B
6y² + 5xy + x² = 0

C
6x² – 5xy + y² = 0

D
None of these

Solution
Question 7
4 / -1

Which of the following second degree equation represents a pair of straight lines ?

A
x² – xy – y² = 1

B
–x² + xy – y² = 1

C
4x² – 4xy + y² = 4

D
x² + y² = 4
Question 8
4 / -1

A general equation of second degree ax² + by² + 2hxy + 2gx + 2fy + c = 0 represents a pair of straight lines if

A
h² = ab

B
h² > ab

C
h² < ab

D

Solution
Question 9
4 / -1

If one of the lines represented by the equation ax² + 2hxy + by² = 0 be y = mx, then

A
bm² + 2hm + a = 0

B
bm² + 2hm – a = 0

C
am² + 2hm + b = 0

D
bm² – 2hm + a = 0

Solution
Question 10
4 / -1

A
9 : 8

B
8 : 9

C
1 : 2

D
2 : 1

Solution