A variable chord is drawn through the origin to the circle `x^2+y^2-2a x=0` . Find the locus of the center of the circle drawn on this chord as diameter.

Options

A. `x^(2) + y^(2) - ax = 0`
B. `x^(2) + y^(2) - ay = 0`
C. `x^(2) + y^(2) + ay = 0`
D. `x^(2) + y^(2) = ay = 0`

Answer

A

Explanation

`(x^(2) + y^(2) - 2ax) + lambda (y - mx) = 0`
`x^(2) + y^(2) - (2a + mlambda) x + lambday = 0`
let centre is `(h,k)`
and `h = ((2a + mlambda)/(2)), k = (-lambda)/(2)`
`lambda = (-2am)/(1+m^(2))`
By eliminating `m`, we get
`x^(2) + h^(2) - ah = 0`
`x^(2) + y^(2) - ax = 0`