Find the length of tangents drawn from the point (4,5) to the circle $x^2+y^2+3x-2y-11=0$?

$\begin{array}{1 1}(a)\;\sqrt{32}&(b)\;\sqrt{12}\\(c)\;\sqrt{30}&(d)\;\sqrt{22}\end{array}$

The equation of given circle is $x^2+y^2+3x-2y-11=0$
$g=-\large\frac{3}{2}$$,f=1,c=11$
Now $S_1=(4)^2+(5)^2+3(4)-2(5)-11=32$
Length of tangent $=\sqrt{S_1}$
$\Rightarrow \sqrt{32}$
Hence (a) is the correct answer.
answered Feb 11, 2014