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  • What is the equation of circle passing through the points of intersection of the two circles <img alt="S_1\: \: and\: \: S_2" src="https://entrancecorner.oncodecogs.com/gif.latex?S_1%5C%3A%20%

What is the equation of circle passing through the points of intersection of the two circles S_1\: \: and\: \: S_2 and the origin.

S_1:x^2+y^2-2x-1=0;S_2=x^2+y^2+2x+2y+1=0

Option: 1

S_1-S_2=0


Option: 2

S_1+S_2=0


Option: 3

S_1+2S_2=0


Option: 4

None of these


Answers (1)

best_answer

Let the circle be

S_1 + K.S_2=0

\Rightarrow x^2+y^2-2x-1+K\left ( x^2+y^2+2x+2y+1 \right )= 0

\Rightarrow \left ( K+1 \right )x^2+ \left( K+1 \right )y^2+2x\left ( K-1 \right )+2Ky+K-1= 0

If this passes through origin we get

0+0+0+0+K-1=0 \Rightarrow K=1

So the equation is S_1 + S_2=0

Posted by

Kuldeep Maurya

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