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10-1.Circle and System of Circles
hard
The equation of the circle which passes through the point of intersection of circles ${x^2} + {y^2} - 8x - 2y + 7 = 0$ and ${x^2} + {y^2} - 4x + 10y + 8 = 0$ and having its centre on $y$ - axis, will be
A
${x^2} + {y^2} + 22x + 9 = 0$
B
${x^2} + {y^2} + 22x - 9 = 0$
C
${x^2} + {y^2} + 22y + 9 = 0$
D
${x^2} + {y^2} + 22y - 9 = 0$
Solution
(c) Using ${S_1} + \lambda {S_2} = 0$,
but its centre is on $y$ – axis.
$i.e.$, $ – 8 – 4\lambda = 0$ or $\lambda = – 2$.
Hence required equation is ${x^2} + {y^2} + 22y + 9 = 0$.
Standard 11
Mathematics
