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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Ellipse

NTA Abhyas 2020 · Mathematics · Ellipse

P _ 1 and P _ 2 are corresponding points on the ellipse x^ 2 16 +...

{P}_{1}

and

{P}_{2}

are corresponding points on the ellipse

\dfrac{x^{2}}{16} + \dfrac{y^{2}}{9} = 1

and its auxiliary circle respectively. If the normal at

{P}_{1}

to the ellipse meets

O{P}_{2}

in

Q

(where

O

is the origin), then the length of

OQ

is equal to

Options

A $3$ units
B $9$ units
C $4$ units
D $7$ units

Correct answer

D. $7$ units

Step-by-step solution

Let,

{P}_{1} = \left(4cos \theta,3sin \theta\right)

and

{P}_{2} = \left(4cos \theta,

4sin

\theta\right)<br />Now, equation of

{P}_{1}Q

is \dfrac{4x}{cos \theta} - \dfrac{3y}{sin \theta} =

7

<br />Equation of

{P}_{2}Q

is \dfrac{x}{cos \theta} = \dfrac{y}{sin \theta}

Q = \left(7cos \theta,7sin \theta\right)

⇒ OQ = 7

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