Let L be a tangent line


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

  1. 11

  2. 14

  3. 16

  4. 20

Correct Option: , 2


Tangent to parabola

$2 \mathrm{y}=2(\mathrm{x}+6)-20$

$\Rightarrow \mathrm{y}=\mathrm{x}-4$

Condition of tangency for ellipse.


$\Rightarrow b=14$

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