- Home
- Standard 11
- Mathematics
10-1.Circle and System of Circles
normal
Lines are drawn from a point $P (-1, 3)$ to a circle $x^2 + y^2 - 2x + 4y - 8 = 0$. Which meets the circle at $2$ points $A$ & $B$, then the minimum value of $PA + PB$ is
A
$6$
B
$8$
C
$10$
D
$12$
Solution
$\mathrm{PA} \times \mathrm{PB}=(\mathrm{PT})^{2}$
where $\mathrm{PT}=$ length of tangent
$(\mathrm{PT})^{2}=(-1)^{2}+3^{2}-2(-1)+4(3)-8=16$
$\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})=16$
$\therefore \mathrm{AM} \geq G M$
$P A+P B \geq 8$
Standard 11
Mathematics
