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Question

# The tangent to the circle x2+y2=5 at the point (1,âˆ’2) touches the circle x2+y2âˆ’8x+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+y2−5=0 is S1=0,x−2y−5=0 It touches the second circle at (x1,y1)∴x1−2y1−5=0 ............(1)The tangent at (x1,y1) to the second circle is S1=0,xx1+yy1−4(x+x1)+3(y+y1)+20=0It passes through (1,−2)∴−3x1+y1+10=0 .........(2)Solving (1) and (2) we getx1=3,y1=−1

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