Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 3

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The ends of a line segment are $P (1, 3)$ and $Q (1, 1)$ . $R$ is a point on the line segment $P Q$ such that $P R : Q R = 1 : λ$ . If $R$ is an interior point of the parabola $y^{2} = 4 x$ , then

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Important Questions on Parabola

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 4

The distance between the focus and directrix of the conic

(\sqrt{3} x - y)^{2} = 48 (x + \sqrt{3} y)

is

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 5

In the adjacent figure, a parabola is drawn to pass through the vertices $B, C$ and $D$ of the square $A B C D$ . If $A (2, 1), C (2, 3)$ , then the focus of this parabola is:

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 6

Length of the latus rectum of the parabola

\sqrt{x} + \sqrt{y} = \sqrt{a}

is

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 7

Consider the parabola

x^{2} + 4 y = 0 .

Let

P (a, b)

be any fixed point inside the parabola and let

S

be the focus of the parabola. Then the minimum value of

S Q + P Q

as point

Q

moves on the parabola is

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 8

The line

x - b + λ y = 0

cuts the parabola

y^{2} = 4 a x (a > 0)

at

P (t_{1})

and

Q (t_{2})

. If

b \in [2 a, 4 a]

, then the range of

t_{1} t_{2}

where

λ \in R - {0}

is

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 9

Let a circle touches the directrix of a parabola

y^{2} = 2 a x

has its centre coinciding with the focus of the parabola. Then the point of intersection of the parabola and circle is

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 10

The equation of the parabola with focus

(a, b)

and directrix

\frac{x}{a} + \frac{y}{b} = 1

, is given by

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 11

Find the length of intercept by the line

4 y = 3 x - 48

on the parabola

y^{2} = 64 x