The equation of the cicle and its chord are respectively `x^(2)+y^(2)= a^(2)` and `x cos alpha +y sin alpha = P` .The equation of the circle of which this chord is a diameter is `:`

Options

A. `x^(2)+y^(2)-2px cos alpha - 2 py sin alpha + 2p^(2)-a^(2)=0`
B. `x^(2)+y^(2)-2px cos alpha - 2 py sin alpha + p^(2)-a^(2)=0`
C. `x^(2)+y^(2)+2px cos alpha + 2 py sin alpha + 2p^(2)-a^(2)=0`
D. none of these

Answer

A

Explanation

The equation of the required circle is
`x^(2)+y^(2)-a^(2)+lambda (x cos alpha + y sin alpha - p ) = 0 " " ...(i)`
The centre of this circle is `(-(lambda )/(2) cos alpha , -(lambda)/(2) sin alpha)` which lies on
`x cos alpha + y sin alpha = p`.
`:. lambda = -2p`
Putting the value of `lambda ` in (i), the equation of the required circle is `x^(2)+y6(2)-a^(2)-2px cos alpha - 2py sin alpha + 2p^(2)=0`.