SATHEE: Circle 5 Question 11

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

$\begin{array}{ll} 12. x^{2} + y^{2} + 8 x - 6 y + 9 = 0 & 13. 10 x - 3 y - 18 = 0 \end{array}$

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

$= a \frac{{(h^{2} + k^{2} - a^{2})}^{3 / 2}}{h^{2} + k^{2}}$

Thus, area of triangle formed by tangents from $(4, 3)$ to the circle $x^{2} + y^{2} = 9$ and their chord of contact

$\begin{aligned} = \frac{3 {(4^{2} + 3^{2} - 9)}^{3 / 2}}{4^{2} + 3^{2}} = \frac{3 (16 + 9 - 9)^{3 / 2}}{25} \\ = \frac{3 (64)}{25} = \frac{192}{25} sq units \end{aligned}$

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Circle 5 Question 11

11. The area of the triangle formed by the tangents from the point (4,3) to the circle x2+y2=9 and the line joining their points of contact is… .

Answer:

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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… .