Find the equation of common tangent of y^2=4ax and x^2=4ay
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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=0x+y+a=0
Hence A is the correct answer.
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=0x+y+a=0
Hence A is the correct answer.
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