    Question

# The lengths of the tangents from (1,0),(2,0),(3,2) to a circle are 1,√7,√2. Then the equation of the circle is

A
x2+y2+6x+17y+6=0
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B
2x2+2y2+6x17y6=0
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C
2x2+2y26x17y6=0
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D
2x2+2y26x17y+6=0
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Solution

## The correct option is A 2x2+2y2+6x−17y−6=0Let equation of circle is x2+y2+2gx+2fy+c=0∴ length of tangent from any point P(x1,y1) to circle isP=√S1=√x21+y21+2gx1+2fy1+cpoint (1,0);L1=1=√1+2g+c2g+c=0...(1)from point (2,0),L2=√7=√4+4g+c4g+c=3...(2)from point (3,2),L3=√2=√13+6g+4f+c6g+4f+c+11=0...(3)From (1) & (2),g=32,c=−3And from (3),9+4f−3+11=0f=−174∴ equation of circle isx2+y2+2×32x−2×174y−3=0⇒2x2+2y2+6x−17y−6=0  Suggest Corrections  0      Similar questions  Related Videos   Family of Straight Lines
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