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Question

A common tangent to 9x216y2=144 and x2+y2=9, is

A
y=37x+157
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B
y=327x+157
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C
y=237x+157
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D
y=37x157
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Solution

The correct option is B y=327x+157
Given curves are 9x216y2=144 and x2+y2=9.
Let the equation of common tangent be y=mx+c.
Since, y=mx+c is a tangent to x2+y2=9,
00+c1+m2=3c2=9(1+m2) (1)
Also, y=mx+c is a tangent to x216y29=1
c2=16m29 (2)
(using condition of tangency)

From (1) and (2), we get
16m29=9+9m2m2=187m=±327
Also, c=±157
Hence, y=327x+157 is one of their common tangent.

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