Parabola Part 1

Equation of tangent to parabola y2=8x at (2,−4) is −4y=4(x+2)
⇒x+y+2=0 ...(i)
Center and radius of circle x2+y2=a is (0,0) and √a respectively.
∵ Eq. (i) is tangent to the circle.
⇒ Perpendicular distance of Eq. (i) from center (0,0)=√a
⇒|

0+0+2

√2

|=√a
⇒ a = 2