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The equation of the circle passing through \( \Large \left(1,\ 1\right) \) and the points of intersection of \( \Large x^{2}+y^{2}+13x-3y=0 \) and \( \Large 2x^{2}+2y^{2}+4x-7y-25=0 \) is:

A) \( \Large 4x^{2}+4y^{2}-30x-10y=25 \)
B) \( \Large 4x^{2}+4y^{2}+30x-13y-25=0 \)
C) \( \Large 4x^{2}+4y^{2}-17x-10y+25=0 \)
D) none of these

Correct Answer:


B) \( \Large 4x^{2}+4y^{2}+30x-13y-25=0 \)

Description for Correct answer:

The required equation of circle is

\( \Large \left(x^{2}+y^{2}+13x-3y\right)+n \left(11x+\frac{1}{2}y+\frac{25}{2}\right) = 0 \)

Passing through \( \Large \left(1,\ 1\right) \)

=> \( \Large 12+n \left(24\right)=0 => n = -\frac{1}{2} \)

On putting in (i), we get

\( \Large x^{2}+y^{2}+13x-3y-\frac{11}{2}x-\frac{1}{4}y-\frac{25}{4} = 0 \)

=> \( \Large 4x^{2}+4y^{2}+52x-12y-22x-y-25 = 0 \)

=> \( \Large 4x^{2}+4y^{2}+30x-13y-25 = 0 \)

Part of solved Circles questions and answers : >> Elementary Mathematics >> Circles

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