JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Parabola

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Let a parabola P be such that its vertex and focus lie on the positive x -axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from

O (0, 0)

to the parabola P which meet P at

S

and

R

, then the area (in sq. units) of

△ S O R

is equal to :

(A)32
(B) $82$
(C)16✓ Correct
(D) $162$

Answer: (C)

Solution

The vertex is

(2, 0)

and the focus

(4, 0)

, so the axis is the

x

-axis with

a = 2

and

y^{2} = 8 (x - 2)

For the curve written as

y^{2} - 8 x + 16 = 0

, the chord of contact of the tangents drawn from

O (0, 0)

y \cdot 0 - 4 (x + 0) + 16 = 0 \Rightarrow x = 4

x = 4

y^{2} = 8 (4 - 2) = 16

, so the points of contact are

S (4, 4)

and

R (4, - 4)

. The chord

S R

has length

8

and lies at a distance

4

from

O

, so

[△ S O R] = \frac{1}{2} \cdot 8 \cdot 4 = 16

The area of

△ S O R

16

square units.

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Single correct option

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JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Parabola

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