The equation of the circle which passes through the points of intersection of the circles $x^{2} + y^{2} - 6x = 0$ and $x^{2} + y^{2} - 6y = 0$ and has its centre at $\left( \frac{3}{2},\frac{3}{2} \right)$, is

Question

Dr. Abubacker · Accepted Answer

(c)
Intersection points of given circles are (0, 0) and (3, 3) let equation of required circle whose centre $\left( \frac{3}{2},\frac{3}{2} \right)$, is
$x^{2} + y^{2} - 3x - 3y + c = 0$
Since, this circle passes through (0, 0), thus equation of circle becomes,
$x^{2} + y^{2} - 3x - 3y = 0$

Q. The equation of the circle which passes through the points of intersection of the circles $x^{2} + y^{2} - 6x = 0$ and $x^{2} + y^{2} - 6y = 0$ and has its centre at $\left( \frac{3}{2},\frac{3}{2} \right)$, is

Explanation

Reviewed by Dr. Abubacker

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