Straight Line and Pair of Straight Lines Test

Result

Straight Line and Pair of Straight Lines Test - 47

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Weekly Quiz Competition

Question 1
4 / -1

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

A
2fgh = bg² + ch²

B
bg² ≠ ch²

C
abc = 2fgh

D
None of these

Solution
Question 2
4 / -1

A
1

B

C
0

D

Solution
Question 3
4 / -1

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

A
x² + y² – ax – by = 0

B
x² + y² + ax + by = 0

C
x² + y² – 2ax – 2by = 0

D
None of these

Solution
Question 4
4 / -1

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

A
x + 4y = 13 and y = 4x – 7

B
4x + y = 13 and 4y = x – 7

C
4x + y = 13 and y = 4x – 7

D
y – 4x = 13 and y + 4x = 7

Solution
Question 5
4 / -1

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

A

B
27 sq. units

C

D
None of these

Solution
Question 6
4 / -1

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

A

B

C

D

Solution
Question 7
4 / -1

A
Straight line

B
Pair of straight lines

C
Circle

D
Ellipse

Solution
Question 8
4 / -1

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

A
x² + 2xy sec 2α + y² = 0

B
x² + 2xy cosec 2α + y² = 0

C
x² – 2xy cosec 2α + y² = 0

D
x² – 2xy sec 2α + y² = 0

Solution
Question 9
4 / -1

A

B

C

D
None of these

Solution
Question 10
4 / -1

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

A
A right-angled triangle

B
An isosceles triangle

C
An equilateral triangle

D
None of these

Solution