Andhra Pradesh Board Solutions for Exercise 5: Exercise 1(e)

Find the pair tangents drawn from $\left(0,0\right)$ to the circle $x^2+y^2+10x+10y+40=0$.

Find the equation of the circle which touches $x^2+y^2-4x+6y-12=0$ at $\left(-1,1\right)$ internally with a radius of $2$.

Find all common tangents of the following pairs of circles $x^2+y^2=9 \text{and} x^2+y^2-16x+2y+49=0$

Find all common tangents of the following pairs of circles $x^2+y^2+4x+2y-4=0 \text{and} x^2+y^2-4x-2y+4=0$

Find the pair tangents drawn from $\left(3,2\right)$ to the circle $x^2+y^2-6x+4y-2=0$.

Find the pair tangents drawn from $\left(1,3\right)$ to the circle $x^2+y^2-2x+4y-11=0$ and also find the angle between them.

Find the pair tangents drawn from the origin to the circle $x^2+y^2+2gx+2fy+c=0$ and hence deduce a condition for these tangents to be perpendicular.

From a point on the circle $x^2+y^2+2gx+2fy+c=0$ two tangents are drawn to the circle $x^2+y^2+2gx+2fy+c{\sin }^2\alpha +\left(g^2+f^2\right){\cos }^2\alpha =0 \left(0<\alpha <\frac{\pi }{2}\right)$. Prove that the angle between them is $2\alpha$.