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Definition of Sets

From the poin...

Question

From the point $P (3, 4)$ tangents $P A$ and $P B$ are drawn to the circle $x^{2} + y^{2} + 4 x + 6 y - 12 = 0 .$ The area of $Δ P A B$ in square units $i . e .$ is

A

\frac{1323}{42}

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B

\frac{1715}{74}

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C

\frac{926}{17}

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D

\frac{1409}{13}

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Solution

The correct option is B $\frac{1715}{74}$
$\begin{matrix} x^{2} + y^{2} + 4 x + 6 y - 12 = 0 {(x + 2)}^{2} + {(y + 3)}^{2} = 25 = {(5)}^{2} a r e a o f Δ P A B = \frac{R l^{3}}{R^{2} + l^{2}} l = \sqrt{{(3)}^{2} + {(4)}^{2} + 4 (3) + 6 (4) - 12} = \sqrt{25 + 12 + 12} = \sqrt{49} = 7 = \frac{5 \times 343}{74} = \frac{1715}{74} O p t i o n B i s c o r r e c t a n s w e r . \end{matrix}$

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