## 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.