Question

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 $24A$ is equal to

Answer 1

BONUS QUESTION :


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

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

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