Let L be a tangent line to the parabola
Question:

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 :

  1. (1) 11

  2. (2) 14

  3. (3) 16

  4. (4) 20


Correct Option: , 2

Solution:

Tangent to parabola $2 y=2(x+6)-20$

$\Rightarrow y=x-4$

Condition of tangency for ellipse. $16=2(1)^{2}+b$

$\Rightarrow b=14$

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