If the area of the triangle formed by the x-axis, the normal and the tangent to the circle \left ( x-2 \right )^{2}+\left ( y-3 \right )^{2}=25 at the point \left ( 5,7 \right ) is A, then 24 A is equal to _______.
Option: 1 1225
Option: 2 1255
Option: 3 1125
Option: 4 1555

Answers (1)

 

(x-2)^{2}+(y-3)^{2}=25

x^{2}-4x+y^{2}-6y=12

Equation of normal 4 x-3 y+1=0

and equation of tangents 3 x+4 y-43=0

\\\text { 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 \\ \\\mathrm{A}=\frac{1225}{24} \\ \\24 \mathrm{~A}=1225

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