Let L be a tangent line to parabola y^{2}=4 x-20 at (6,2) . If L is also a tangent to ellipse

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10-2. Parabola, Ellipse, Hyperbola

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Let $L$ be a tangent line to the parabola $y^{2}=4 x-20$ at $(6,2)$ . If $L$ is also a tangent to the ellipse $\frac{ x ^{2}}{2}+\frac{ y ^{2}}{ b }=1,$ then the value of $b$ is equal to ..... .

A

$11$

B

$14$

C

$16$

D

$20$

(JEE MAIN-2021)

Solution

Tangent to parabola

$2 y=2(x+6)-20$

$\Rightarrow y=x-4$

Condition of tangency for ellipse.

$16=2(1)^{2}+ b$

$\Rightarrow b =14$

Standard 11

Mathematics

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