JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-23
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)