36.
The equation of any tangent to y2=4ax is
y=mx+ma
If it touches x2=4ay then, the equation.
⇒x2=4a(mx+ma) has equal roots.
⇒mx2−4am2x−4a2=0 has equal roots
If the roots are equal, the discriminant is equal to 0
i.e.,b2−4ac=0
⇒16a2m4+16a2m=0
⇒16a2m4=−16a2m
m=−1
Putting m=−1 in y=mx+am we get,
y=−x−a
⇒x+y+a=0 This is the common tangent to the two parabola.