The equation of the circle having its centre on the line $x - 2 y - 3 = 0$ and passing through the point of intersection of the circles
$x^{2} + y^{2} - 2 x - 4 y + 1 = 0$ and $x^{2} + y^{2} - 4 x - 2 y + 4 = 0$ is

Question

The equation of the circle having its centre on the line $x - 2 y - 3 = 0$ and passing through the point of intersection of the circles

$x^{2} + y^{2} - 2 x - 4 y + 1 = 0$ and $x^{2} + y^{2} - 4 x - 2 y + 4 = 0$ is

Infinity Learn · Accepted Answer

The equation of a circle passing through $$tr-$$.:intersectionof the two given circles is   $$x2+y2$$−$$2x$$−$$4y+1+$$λ$$x2+y2$$−$$4x$$−$$2y+4=0$$⇒$$x2+y2$$−$$2x1+2$$λ$$1+$$λ−$$2y(2+$$λ$$)1+$$λ$$+1+4$$λ$$1+$$λ÷$$0$$…(i)The$$ $$co-ordinates$$ of its centre are $$1+2$$λ$$1+$$λ, $$2+$$λ$$1+$$λSince the centre lies on $$x+2y$$−$$3=0$$.∴ $$1+2$$λ$$+4+2$$λ−$$3$$−$$3$$λ$$=0$$⇒λ$$=$$−$$2Putting$$ λ$$=$$−$$2$$ in $$(i), we obtain that the required circle is    $$x2+y2$$−$$6x+7=0$$.

The equation of the circle having its centre on the line $x - 2 y - 3 = 0$ and passing through the point of intersection of the circles
$x^{2} + y^{2} - 2 x - 4 y + 1 = 0$ and $x^{2} + y^{2} - 4 x - 2 y + 4 = 0$ is

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The equation of the circle having its centre on the line x-2y-3=0 and passing through the point of intersection of the circlesx2+y2−2x−4y+1=0 and x2+y2−4x−2y+4=0 is

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The equation of the circle having its centre on the line $x - 2 y - 3 = 0$ and passing through the point of intersection of the circles
$x^{2} + y^{2} - 2 x - 4 y + 1 = 0$ and $x^{2} + y^{2} - 4 x - 2 y + 4 = 0$ is