Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.1>Q 2

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The axis of parabola $9 y^{2} - 16 x - 12 y - 57 = 0$ is

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Important Questions on Parabola

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.1>Q 3

The equation of the directrix of the parabola

y^{2} + 4 y + 4 x + 2 = 0

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.1>Q 4

The equation of the directrix of the parabola

x = - 2 a t, y = - a t^{2}, t \in R,

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.1>Q 5

If the parabola

y^{2} = 4 a x

passes through

(3, 2) .

Then the length of its latus rectum is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.1>Q 6

The focal distance of a point on the parabola

y^{2} = 4 x

and above its axis, is

10

units. Its coordinates are

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.1>Q 7

The endpoints of the latus rectum of a parabola are

(7, 5)

and

(7, 3),

then possible coordinates of its vertex are

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.2>Q 1

A tangent to the parabola

y^{2} = 4 a x

is inclined at

\frac{π}{3}

with the axis of the parabola. The point of contact is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.2>Q 2

The equation of tangent to the parabola

y^{2} = 9 x

which goes through the point

(4, 10),

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.2>Q 3

Let

A, B

and

C

be three points taken on the parabola

y^{2} = 4 a x

with coordinates

(a t_{i}^{2}, 2 a t_{i})

i = 1, 2, 3,

where

t_{1}, t_{2}

and

t_{3}

are in

AP

. If

A A^{'}, B B^{'}

and

C C^{'}

, are focal chords and coordinates of

A^{'}, B^{'}, C^{'}

are

(a t_{i}^{' 2}, 2 a t_{i}^{'}), i = 1, 2, 3

then

t_{1}^{'}, t_{2}^{'}

and

t_{3}^{'}

are in