let x2 +y2 -4x-2y-11=0 be a circle.a pair of tangents from the points (4,5) with a pair of radii form a quadrilateral of area...

12

• means its centre at2,1 and radii 4.it is at adis.from 2 so area of one triangle from quadilateral is 8.so another is also a right angled triangle  so its area 4. so total area 12

First draw a circle with radius 4 and centre as (2,1), this we can find. From point p(4,5) 2 tangents are drawn. Let upper tangents or 1st tangents touches the circle at point T and lower or 2nd tangents touches the circle at point Q. Let center be C. AS we know CT or CQ are radius which is 4 units. Draw a straight line to the centre of circle C. By pythogoras theorem we can find length of upper and lower tangents. We get PT=2 units. And PQ =2 units. Let PT be A, PQ be B, CQ be C, and QP be D. As we know ar of quadrilateral is 0.5*(ad+bc). A=2, B=2,C=4 and D=4. Putt the values 0.5*(8+8)=8sq units