Circle 5 Question 11
11. The area of the triangle formed by the tangents from the point $(4,3)$ to the circle $x^{2}+y^{2}=9$ and the line joining their points of contact is… .
$(1987,2 M)$
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Answer:
Correct Answer: 11. $\frac{192}{25}$ sq units
$\begin{array}{ll}\text { 12. } x^{2}+y^{2}+8 x-6 y+9=0 & \text { 13. } 10 x-3 y-18=0\end{array}$
Solution:
- Area of triangle formed by the tangents from the point $(h, k)$ to the circle $x^{2}+y^{2}=a^{2}$ and their chord of contact
$$ =a \frac{\left(h^{2}+k^{2}-a^{2}\right)^{3 / 2}}{h^{2}+k^{2}} $$
Thus, area of triangle formed by tangents from $(4,3)$ to the circle $x^{2}+y^{2}=9$ and their chord of contact
$$ \begin{aligned} & =\frac{3\left(4^{2}+3^{2}-9\right)^{3 / 2}}{4^{2}+3^{2}}=\frac{3(16+9-9)^{3 / 2}}{25} \\ & =\frac{3(64)}{25}=\frac{192}{25} \text { sq units } \end{aligned} $$
