Conic Section Test

Result

Conic Section Test - 29

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Weekly Quiz Competition

Question 1
4 / -1

If two tangents drawn from the point (α, β) to the parabola y² = 4x be such that the slope of one tangent is double of the other, then

A

B

C

D
none of these.

Solution
Question 2
4 / -1

y + h = m₁(x + a) and y + k = m₂ (x + a) are two tangents to the parabola y² = 4ax ; then

A
m₁ + m₂ = 0

B
m₁ m₂ = 1

C
m₁ m₂ = −1

D
none of these
Question 3
4 / -1

The area of the triangle formed by the tangent and the normal to the parabola y² = 4ax, both drawn at the same end of the latus rectum and the axis of the parabola is

A

B
2a²

C
4a²

D
none of these

Solution
Question 4
4 / -1

Let P, Q, R be three pts. on a parabola, normals at which are concurrent. The centroid of the ∆ PQR must lie on

A
a line parallel to the directrix

B
the axis of the parabola

C
a line of slope 1 passing thro’ the vertex

D
none of these

Solution
Question 5
4 / -1

The vertex of the parabola y² = 8x is at the centre of a circle and the parabola cuts the circle at the ends the latus rectum. Then the equation of the circle is

A
x² + y² = 4

B
x² + y² = 20

C
x² + y² = 80

D
none of these

Solution
Question 6
4 / -1

If O is the pole of the chord PQ of a parabola, then the perpendicular from P, O, Q on any tangent to the curve are in

A
A.P.

B
G.P.

C
H.P.

D
none of these

Solution
Question 7
4 / -1

The ends of a line segment are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that PR : RQ = 1 : λ. If R is an interior point of the parabola y² = 4x , then

A
λ ∈ (0, 1)

B

C

D
none of these.

Solution
Question 8
4 / -1

A
A hyperbola

B
An ellipse

C
A pair of straight lines

D
A rectangular hyperbola

Solution
Question 9
4 / -1

A
(2, 3)

B
(2, –3)

C
(–2, 3)

D
(–2, –3)

Solution
Question 10
4 / -1

The equation of the conic with focus at (1, –1), directrix along x – y = 0 and with eccentricity √2 is

A

B

C

D

Solution