The point $T(6,-2)$ lies outside the circle $(x-1)^2+(y+2)^2=9$. The tangents from $T$ touch t

Question

The point $T(6,-2)$ lies outside the circle $(x-1)^2+(y+2)^2=9$. The tangents from $T$ touch the circle at $A$ and $B$. Find the equations of both tangents.[4] Find the coordinates of $A$ and $B$.[3] Find the exact area of triangle $TAB$.[2]

Accepted Answer

(a) $y+2=\pm\dfrac34(x-6)$. (b) $\left(\dfrac{14}{5},\dfrac25\right)$, $\left(\dfrac{14}{5},-\dfrac{22}{5}\right)$. (c) $\dfrac{192}{25}$ square units.

Two tangents from an external point

Two tangents from an external point

Solution:

Solution locked