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Question

The circle x2+y28x=0 and hyperbola x29y24=1 intersect at the points A and B.
Equation of a common tangent with positive slope to the circle as well as to the hyperbola is


A

2x5y20=0

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B

2x5y+4=0

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C

3x4y+8=0

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D

4x3y+4=0

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Solution

The correct option is B

2x5y+4=0


Equation of tangent to hyperbola having slope m is
y=mx+9m24 ...(i)
Equation of tangent to circle is
y=m(x4)+16m2+16 ...(ii)
Eqs. (i) and (ii) will be identical for m=25 satisfy.
Equation of common tangent is 2x5y+4=0.


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