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Question

The tangent to the circle x2+y2=5 at the point (1,2) touches the circle x2+y28x+6y+20=0 at the point

A
(3,1)
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B
(3,1)
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C
(3,1)
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D
(3,1)
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Solution

The correct option is C (3,1)
The tangents at (1,2) on the circle x2+y25=0 is S1=0,x2y5=0
It touches the second circle at (x1,y1)
x12y15=0 ............(1)
The tangent at (x1,y1) to the second circle is S1=0,
xx1+yy14(x+x1)+3(y+y1)+20=0
It passes through (1,2)
3x1+y1+10=0 .........(2)
Solving (1) and (2) we get
x1=3,y1=1

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