Question

Two common tangents to the circle x^2+y^2=2a^2 and parabola y^2=4ax are

Answer 1

solution

x²+y²=2a² and y²=4ax

using implicit method

⇒ x²+y²=2a²

2x+2ydy/dx=0

⇒ dy/dx=-2x/2y,

⇒ dy/dx=-x/y

for the parabolar

y²=4ax

⇒ 2ydy/dx=4a

dy/dx=4a/2y

dy/dx=2a/y