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10-2. Parabola, Ellipse, Hyperbola
medium
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