Conic Section Test

Result

Conic Section Test - 8

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

The equation of the chord of the circle x² + y² - 4x = 0, whose mid - point is (1, 0) is

A
y = 2

B
y = 1

C
x = 2

D
x = 1
Question 2
4 / -1

The middle point of the chord x + 3y = 2 of the conic x² + xy - y² = 1, is

A
(5, -1)

B
(1, 1)

C
(2, 0)

D
(-1, 1)
Question 3
4 / -1

The mid - point of the chord 4 x - 3y = 5 of the hyperbola 2 x² - 3y² = 12, is

A

B
(2, 1)

C

D

Solution
Question 4
4 / -1

The length of the common chord of the parabolas y² = x and x² = y, is

A
2√2

B
1

C
√2

D
1/√2
Question 5
4 / -1

The locus of middle points of chords of hyperbola
3x² - 2y² + 4x - 6y = 0 parallel to y = 2x, is

A
3x - 4y = 4

B
3y - 4x + 4 = 0

C
4x - 3y = 3

D
3x - 4y = 2
Question 6
4 / -1

If a focal chord of parabola y² = 16x cuts it at points (f, g) and (h, k). Then f, h is equal to

A
12

B
16

C
14

D
None of these

Solution
Question 7
4 / -1

If the parabola y² = 4ax, the length of the chord passing through the vertex inclined to the axis at π/4, is

A
4a√2

B
2a√2

C
a√2

D
a
Question 8
4 / -1

If the chords of contact of tangents from two points (x₁, y₁) and (x₂, y₂) to the hyperbola 4x² - 9y² - 36 = 0 are right angles, then

A
9/4

B
- (9/4)

C
81/16

D
- (81/9)
Question 9
4 / -1

If a focal chord of the parabola y² = ax is 2x - y - 8 = 0, then the equation of the directrix is

A
x + 4 = 0

B
x - 4 = 0

C
y - 4 = 0

D
y + 4 = 0
Question 10
4 / -1

The length of the chord of the parabola y² = 4ax, which passes through the vertex and makes an angle α with the axis of the parabola is

A
4a cos α cosec² α

B
4a α cosec² α

C
a cos α cosec² α

D
a cos α cosec α