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Question

The equation of common tangent to the parabolas y2=4x and x2=4y is

A
xy+1=0
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B
x+y1=0
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C
x+y+1=0
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D
xy1=0
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Solution

The correct option is C x+y+1=0
Equation of any tangent to y2=4x:
y=mx+1m
Equation of tangent to x2=4y:
y=mxm2
They represent same tangents, so
1m=m2
m=1
Equation of tangent;
y=x1
x+y+1=0

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