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

Answer: 1225

Equation of normal $4x-3y+1=0$
and equation of tangents $3x+4y-43=0$
Area of triangle
$=\frac{1}{2}\left(\frac{43}{3}+\frac{1}{4}\right)\times (7)$
$=\frac{1}{2}\left(\frac{172+3}{12}\right)\times 7$
$A=\frac{1225}{24}$
$24A=1225$
* as positive $x$ -axis is given in the question so question should be bonus.