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Question

The equation of common tangent to the curves y2=16x and xy= 4, is :

A
x2y+16=0
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B
x+y+4=0
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C
2xy+2=0
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D
xy+4=0
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Solution

The correct option is D xy+4=0
Let the equation of the tangent to y2=16x be
y=mx+4m
This is also a tangent to the curve xy=4
x(mx+4m)=4m2x2+4x+4m=0

For tangent,
D=01616m3=0m=1
So, equation of common tangent is y=x+4

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