Telangana Board Solutions for Exercise 2: Exercise 1(b)

Find the power of the point $P$ with respect to the circle $S=0$ when $P=(2,4)$ and $S\equiv x^2+y^2-4x-6y-12$

Find the length of tangent from $P$ to the circle $S=0$ when $P=(-2,5)$ and $S\equiv x^2+y^2-25$

Find the length of tangent from $P$ to the circle $S=0$ when $P=(0,0)$ and $\mathrm{S}=x^2+y^2-14x+2y+25$

Find the length of tangent from $P$ to the circle $S=0$ when $P=(2,5)$ and $\mathrm{S}\equiv x^2+y^2-5x+4y-5$

If the length of the tangent from $\left(5,4\right)$ to the circle $x^2+y^2+2ky=0$ is $1$ then find $k$.

If the length of the tangent from $\left(2,5\right)$ to the circle $x^2+y^2-5x+4y+k=0$ is $\sqrt{37}$ then find $k$.

If a point $\mathrm{P}$ is moving such that the lengths of tangents drawn from $\mathrm{P}$ to the circles ${\mathrm{x}}^2+{\mathrm{y}}^2-4\mathrm{x}-6\mathrm{y}-12=0$ and ${\mathrm{x}}^2+{\mathrm{y}}^2+6\mathrm{x}+18\mathrm{y}+26=0$ are in the ratio $2:3$ then find the equation of the locus of $\mathrm{P}$.

If a point $\mathrm{P}$ is moving such that the lengths of tangents drawn from $\mathrm{P}$ to the circles ${\mathrm{x}}^2+{\mathrm{y}}^2+8\mathrm{x}+12\mathrm{y}+15=0$ and ${\mathrm{x}}^2+{\mathrm{y}}^2-4\mathrm{x}-6\mathrm{y}-12=0$ are equal then find the equation of the locus of $\mathrm{P}$.