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(C) Let the circle intersect the $x$-axis at $A$ and the $y$-axis at $B$.Since the circle passes through the origin $O(0,0)$ and makes intercepts of l

Vedclass · Accepted Answer

$x^2 + y^2 - 5x - 5y = 0$

Vedclass · Answer

(C) Let the circle intersect the $x$-axis at $A$ and the $y$-axis at $B$.Since the circle passes through the origin $O(0,0)$ and makes intercepts of length $5$ on both axes,the coordinates are $A(5,0)$ and $B(0,5)$.Since $\angle AOB = 90^{\circ}$,the segment $AB$ is the diameter of the circle.The equation of a circle with diameter endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $(x - x_1)(x - x_2) + (y - y_1)(y - y_2) = 0$.Substituting the points $(5,0)$ and $(0,5)$:$(x - 5)(x - 0) + (y - 0)(y - 5) = 0$$x(x - 5) + y(y - 5) = 0$$x^2 - 5x + y^2 - 5y = 0$$x^2 + y^2 - 5x - 5y = 0$.

Find the equation of a circle passing through the origin and making intercepts of length $5$ on both axes.

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