The intercept on the line y=x by the circle x^2+y^2-2x=0 is AB.

Question

The intercept on the line $y=x$ by the circle $x^2+y^2-2x=0$ is $AB$. The equation of the circle on $AB$ as a diameter is:

Accepted Answer

Solving $y=x$ and the circle

${x^2} + {y^2} - 2x = 0,$ we get

$x = 0,y = 0$ and $x=1,$ $y=1$

$$\therefore$$ Extremities of diameter of the required circle are

$$\left( {0,0} \right)$$ and $$\left( {1,1} \right)$$. Hence, the equation of circle is

$$\left( {x - 0} \right)\left( {x - 1} \right) + \left( {y - 0} \right)\left( {y - 1} \right) = 0$$

$$ \Rightarrow {x^2} + {y^2} - x - y = 0$$

Solutions · 1