Question

The equation of common tangent to the parabola y2=4ax and x2=4ay is

Answer 1

The equation of any tangent to y2=4axy2=4ax

y=mx+amy=mx+am

If it touches x2=4ayx2=4ay then, the equation.

x62=4a(mx+am)x62=4a(mx+am) has equal roots.

=> mx2−4am2x−4a2=0mx2−4am2x−4a2=0

it has equal roots

=> 16a2m4=−16a2m16a2m4=−16a2m

=> m=−1m=−1

Putting m=−1m=−1 in y=mx+amy=mx+am we get,

y=−x−ay=−x−a or x+y+a=0

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