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Question

Equation of the common tangent to the ellipse x216+y29=1 and the circle x2+y2=12 is

A
2y=3x+21
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B
3y=2x+21
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C
3y=2x21
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D
y
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Solution

The correct option is A 2y=3x+21
Equation of tangent to the ellipse x216+y29=1 is y=mx±16m2+9
mxy±16m2+9=0
If it is also Tangent to the circle x2+y2=12 then r = d holds good,
12=16M2+9M2+1
12(m2+1)=16m2+9
m2=34m=±32
Tangent is 2.y=3x±21

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