A tangent line L is drawn at the point (2,-4) on the parabola y^2=8x.

Question

A tangent line $L$ is drawn at the point $(2,-4)$ on the parabola $y^2=8x$. If the line $L$ is also tangent to the circle $x^2+y^2=a$, then $a$ is equal to \_\_\_\_\_\_\_\_.

Answer: 2

Accepted Answer

Tangent at $(2,-4)$: $-4y=4(x+2)\Rightarrow x+y+2=0$.

Distance from $(0,0)$ to this line equals $\sqrt a$: $\dfrac{|2|}{\sqrt2}=\sqrt a\Rightarrow a=2$.

Solutions · 1