From a point `R(5,8)` , two tangents `R Pa n dR Q` are drawn to a given circle `S=0` whose radius is 5. If the circumcenter of triangle `P Q R` is (2, 3), then the equation of the circle `S=0` is (a)`x^2+y^2+2x+4y-20=0` (b) `x^2+y^2+x+2y-10=0` (c) `x^2+y^2-x+2y-20=0` (d )`x^2+y^2+4x-6y-12=0`

Options

A. `x^(2)+y^(2)+2x+4y-20=0`
B. `x^(2)+y^(2)+x+2y-10=0`
C. `x^(2)+y^(2)-x-2y-20=0`
D. `x^(2)+y^(2)-4x-6y-12=0`

Answer

1

Explanation

Let C be the center of the given circle.
Then, the circumcircle of `DeltaRPQ` passes through C.
Therefore, (2,3) is the midpoint of RC.
Thus, the coordinates of C are `(-1,-2)`.
Hence, the equation of the circle is `x^(2)+y^(2)+2x+4y-20=0`