Question

If `y=2x` is a chord of the circle `x^2+y^2-10 x=0` , find the equation of a circle with this chord as diameter.

Answer 1

`x^2+y^2-10x=0`
`x^2(2x)^2-10x=0`
`x^2+4x^2-10x=0`
`5x^2-10x=0`
`5x(x-2)=0`
`(x-x_1)(x-x_2)+(y-y_1)(y-y_1)=0`
`(x-0)(x-2)+(y-0)(y-4)=0`
`x(x-2)+y(y-4)=0`
`x^2+y^2-2x-4y=0`.