question_answer

Let \[{{x}^{2}}+{{y}^{2}}+2x-4y-4=0\]be a circle. A pair of tangents from the point P(2,3) with a pair of radii form a quadrilateral of area equals

A)  4                                

B)  3

C)  2                                

D)  1      

Correct Answer: B

Solution :

The equation of circle is \[{{(x+1)}^{2}}+{{(y-2)}^{2}}=9\]             \[\therefore \] Length of tangent form P(2, 3) is             \[=\sqrt{9+1-9}=1=PA=PB\] \[\therefore \] Area of quadrilateral = 2 area \[(\Delta PAC)\] \[=2\times \frac{1}{2}\times 1\times 3\,=3\] (sq. units)