please answerA common tangent drawn to a circle x2+y2=c2 and a parabola y2=4ax.If the angle which this tangent makes with twe x axis is pi/4 then the relationship between c and a is?

Let assume the eqn of tangent is y = mx + a/m

tangent makes 45 deg with x axis hence slope will be 1 => m =1

henceeqn of tangent is y = x + a

and this line tangent to circle also so perpendicular distance from center to tangent equals radius

So,

a/root2 = c

hence 2c^2 = a^2

Thank You!