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From a point R(5, 8) two tangents RP and...

From a point R(5, 8) two tangents RP and RQ are drawn to a given circle s=0 whose radius is 5. If circumcentre of the triangle PQR is (2, 3), then the equation of 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`

Text Solution

Verified by Experts

The correct Answer is:
1

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`
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