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NTA Abhyas 2020

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

NTA Abhyas 2020 · Mathematics · Ellipse

From the point P (3,4) pair of tangents PA and PB are drawn to the...

From the point

P

\left(3,4\right)

pair of tangents

PA

and

PB

are drawn to the ellipse

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

If

AB

intersects

y

-axis at

C

and

x

-axis at

D

, then

OC \cdotOD is equal to (where

O

is the origin) From the point P (3,4) pair of tangents PA and PB are drawn to the ellipse x^ 2 16 + y^ 2 9 =1. If AB intersects y

From the point P (3,4) pair of tangents PA and PB are drawn to the ellipse x^ 2 16 + y^ 2 9 =1. If AB intersects y

Options

A $9$
B $18$
C $8$
D $12$

Correct answer

D. $12$

Step-by-step solution

Equation of the chord of contact of the tangents from point&

P

to the given ellipse is&

\dfrac{3x}{16} + \dfrac{4y}{9} = 1

∴ C \left(0, \dfrac{9}{4}\right),D \left(\dfrac{16}{3},0\right)

From the point P (3,4) pair of tangents PA and PB are drawn to the ellipse x^ 2 16 + y^ 2 9 =1. If AB intersects y

⇒ OC \timesOD = \dfrac{9}{4} \times \dfrac{16}{3} =12

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