Conic Section Test

Result

Conic Section Test - 27

Score
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Weekly Quiz Competition

Question 1
4 / -1

The equation of the director circle of the hyperbola 9x - 16y² = 144 is

A
x² + y² = 7

B
x² + y² = 9

C
x² + y² = 16

D
x² + y² = 25
Question 2
4 / -1

If P(at², 2at) is one end of a focal of the parabola y² = 4ax, then the length of the focal chord is

A

B

C

D

Solution
Question 3
4 / -1

Locus of mid - point of any focal chord y² = 4ax is

A
y² = a(x - 2a)

B
y² = 2a(x - 2a)

C
y² = 2a(x - a)

D
None of these
Question 4
4 / -1

The equation of the chord joining two points (x ₁, y₁) and (x ₂, y₂) on the rectangular hyperbola xy = c² is

A

B

C

D
Question 5
4 / -1

Find the measure of angle between the asymptotes of x² - y² = 16

A
π/4

B
π/3

C
π/6

D
π/2
Question 6
4 / -1

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x² + 9y² = 9 meets its auxiliary circle at the point M. Then, the area of the triangle with vertices A, M and the origin O is

A
31/10

B
29/10

C
21/10

D
27/10
Question 7
4 / -1

The product of perpendicular drawn from any point of a hyperbola to its asymptotes is

A

B

C

D
Question 8
4 / -1

Given the two ends of the latus rectum, the maximum number of parabolas that can be drawn is

A
1

B
2

C
0

D
infinite

Solution
Question 9
4 / -1

If the vertex of the parabola is (2, 0) and extremities of the latus rectum are (3, 2) and (3,–2), then the equation of the parabola is

A
y² = 2x ‒ 4

B
y² = 4y ‒ 8

C
y² = 4x ‒ 8

D
none of these.

Solution
Question 10
4 / -1

The equation of the parabola whose vertex and focus are on the positive side of the x–axis at distances α and b respectively from the origin is

A
y² = 4 (b ‒ a)(x ‒ a)

B
y² = 4 (a ‒ b)(x ‒ b)

C
x² = 4 (b ‒ a)(y ‒ a)

D
none of these

Solution