Q. Let $AB$ be the intercept of the line $y = x$ the circle$x^{2} + y^{2} - 2x = 0$. Then, the equation of the circle with $AB$ as its diameter is
A) $x^{2} + y^{2} - x - y = 0$
B) $x^{2} + y^{2} + x + y = 0$
C) $x^{2} + y^{2} + 2(x - y) = 0$
D) $x^{2} + y^{2} - 2x + y = 0$
Explanation
(a)
The coordinate of the point of intersection of line $y = x$ and circle $x^{2} + y^{2} - 2x = 0$ is $A(0,\ 0)$ and $B(1,\ 1)$
$\therefore$ Equation of circle with $AB$ as its diameter is
$x(x - 1) + y(y - 1) = 0$
$\Rightarrow \ \ \ x^{2} + y^{2} - x - y = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.