If the area of the triangle formed by the positive $x -$ axis, the normal and the tangent to the circle $(x - 2)^{2} + (y - 3)^{2} = 25$ at the point $(5, 7)$ is $A,$ then $24 A$ is equal to

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Solution

BONUS QUESTION :

Equation of normal at $P$ is
$(y - 7) = (\frac{7 - 3}{5 - 2}) (x - 5)$
$\Rightarrow 3 y - 21 = 4 x - 20$
$\Rightarrow 4 x - 3 y + 1 = 0$
$\Rightarrow M$ is $(- \frac{1}{4}, 0)$

Equation of tangent at $P$ is
$(y - 7) = - \frac{3}{4} (x - 5)$
$\Rightarrow 4 y - 28 = - 3 x + 15$
$\Rightarrow 3 x + 4 y = 43$
$\Rightarrow N$ is $(\frac{43}{3}, 0)$

The question is WRONG. The normal cuts at a point on the negative axis.

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