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Question

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

A
x+y+a=0
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B
x+ya=0
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C
xy+a=0
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D
xya=0
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Solution

The correct option is A x+y+a=0
The equation of any tangent to y2=4ax is y=mx+am, if it touches x2=4ay,
then the equation x2=4a(mx+am) has equal roots or, mx24am2x4a2=0 has equal roots

16a2m4=16a2mm=1(m0)

Putting m=1 in y=mx+am, we get y=xa or, x+y+a=0

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