A) \[\frac{24}{25}\]
B) 0
C) \[\frac{625}{24}\]
D) \[-\left( \frac{24}{25} \right)\]
Correct Answer: C
Solution :
The equation of the tangent at \[P(3,\,4)\] to the circle\[{{x}^{2}}+{{y}^{2}}=25\] is \[3x+4y=25\], which meets the co-ordinate axes at \[A\left( \frac{25}{3},\,0 \right)\] and \[B\,\left( 0,\,\frac{25}{4} \right)\]. If O be the origin, then the \[\Delta OAB\] is a right angled triangle with \[OA=25/3\] and \[OB=25/4\]. Area of the \[\Delta OAB=\frac{1}{2}\times OA\times OB\] = \[\frac{1}{2}\times \frac{25}{3}\times \frac{25}{4}\]=\[\frac{625}{24}\].You need to login to perform this action.
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