Circle And System Of Circles Question 64
Question: The value of c, for which the line $ y=2x+c $ is a tangent to the circle $ x^{2}+y^{2}=16 $ , is
[MP PET 2004; Karnataka CET 2005]
Options:
A) $ \frac{24}{25} $
B) 0
C) $ \frac{625}{24} $
D) $ -( \frac{24}{25} ) $
Show Answer
Answer:
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( \frac{25}{3},,0 ) $ and $ B,( 0,,\frac{25}{4} ) $ . 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} $ .
BETA
