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NTA Abhyas 2020

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

NTA Abhyas 2020 · Mathematics · Ellipse

If a tangent having slope 2 of the ellipse x^ 2 a^ 2 + y^ 2 b^ 2 =...

If a tangent having slope

2

of the ellipse

\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1

is normal to the circle

x^{2} + y^{2} + 4x + 1 = 0,

then the value of

4a^{2} + b^{2}

is equal to

Options

A $4$
B $2$
C $16$
D $8$

Correct answer

C. $16$

Step-by-step solution

Equation of tangent is

y = 2x \pm \sqrt{4a^{2} + b^{2}}

This is normal to the circle

x^{2} + y^{2} + 4x + 1 = 0

This tangent passes through \left(- 2,0\right)

<br />

0 = - 4 \pm \sqrt{4a^{2} + b^{2}} ⇒ 4a^{2} + b^{2} = 16

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