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The centre of a circle passing through the points (0, 0) and (1, 0)and touching the circle x^2+y^2+2x-6y=6

The centre of a circle passing through the points (0, 0) and (1, 0)and touching the circle x^2+y^2+2x-6y=6

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1 Answers

Sunil Raikwar
askIITians Faculty 45 Points
7 years ago
Let the equation of circle be x^2+y^2+2gx+2fy+c=0, it passes through (0,0) therefore c=0
it is also passes through(1,0) therefore
1+2g=0
g=-1/2
since this circle touches the circle x^2+y^2+2x-6y=6
therefore distance between their centres equal to sum of their radius
squreroot[(-g-1)^2+(-f+3)^2]=squreroot(g^2+f^2)+2 & g=-1/2 find f by putting the value of g.

Thanks & Regards
Sunil Raikwar
askIITians faculty

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