Power of a point wrt Circle - Practice Questions & MCQ

Power of a point wrt Circle

The power of a point $\mathrm{P}(\mathrm{a}, \mathrm{b})$ with respect to the circle $S: \mathrm{x}^2+\mathrm{y}^2+2 \mathrm{gx}+2 \mathrm{fy}+\mathrm{c}=0$ is $\mathrm{S}_1$, where $\mathrm{S}_1: \mathrm{a}^2+\mathrm{b}^2+2 \mathrm{ga}+2 \mathrm{fb}+\mathrm{c}=0$

We know $\mathrm{PA} \cdot \mathrm{PB}=(\mathrm{PT})^2$
Also we know that $\mathrm{PT}=\sqrt{S_1}$
So, $\mathrm{PA} \cdot \mathrm{PB}=\mathrm{PT}^2=\mathrm{S}_1$

Chord of Contact

$S$ is a circle and $P\left(x_1, y_1\right)$ be an external point to a circle $S$. A and $B$ are the points of contact of the tangents drawn from P to circle S . Then the chord AB is called the chord of contact of the circle S drawn from an external point $P$.

To get the equation of chord of contact of external point $\mathrm{P}\left(\mathrm{x}_1, \mathrm{y}_1\right)$ with respect to the circle $x^2+y^2+2 g x+2 f y+c=0$, we use the formula $\mathrm{T}=0$ So the equation of chord of contact is $x x_1+y y_1+g\left(x+x_1\right)+f\left(y+y_1\right)+c=0$