Two common tangents to the circle x^2+y^2=2 a^2 and parabola y^2=8 a x are

Step-by-step solution

Any tangent to the parabola y^2=8 a x is y=m x+ 2 a m If (i) is a tangent to the circle, x^2+y^2=2 a^2 then, 2 a= 2 a m m^2+1 m^2 (1+m^2 )=2 (m^2+2 ) (m^2-1 )=0 ; m= 1 So, y= (x+2 a)