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Question

Area enclosed by the common tangents of circle x2+y2=4 and ellipse 3x2+5y2=15 is

A
4
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B
8
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C
16
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D
32
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Solution

The correct option is C 16
Equation of tangent
y=mx±5m2+3
mxy±5m2+3=0

Distance from (0,0)=2
2=5m2+31+m2
Hence m=1,1
So four tangents are :
y=x±22y=x±22
The required Area
=4×12×22×22=16

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