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Standard XII

Mathematics

Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line

Find the equa...

Question

Find the equation of the circle passing through the points of intersection of the circles
$x^{2} + y^{2} - 6 x + 2 y + 4 = 0$
and $x^{2} + y^{2} + 2 x - 4 y - 6 = 0$
and with its centre on the line y = x.

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Solution

$S + λ S_{2} = 0, l a m b d a = 4 / 3$
$7 (x^{2} + y^{2}) - 10 x - 10 y - 12 = 0$

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Find the equation of the circle passing through the points of intersection of the circles x2+y2−6x+2y+4=0and x2+y2+2x−4y−6=0 and with its centre on the line y = x.

S+λS2=0,lambda=4/37(x2+y2)−10x−10y−12=0

Find the equation of the circle passing through the points of intersection of the circles
$x^{2} + y^{2} - 6 x + 2 y + 4 = 0$
and $x^{2} + y^{2} + 2 x - 4 y - 6 = 0$
and with its centre on the line y = x.

$S + λ S_{2} = 0, l a m b d a = 4 / 3$
$7 (x^{2} + y^{2}) - 10 x - 10 y - 12 = 0$