Conic-Sections Question 556
Question: If the equation of the common tangent at the point $ (1,-1) $ to the two circles, each of radius 13, is $ 12x+5y-7=0 $ then the centres of the two circles are
Options:
A) $ (13,4),(-11,6) $
B) $ (13,4),(-11,-6) $
C) $ (13,-4),(-11,-6) $
D) $ (-13,4),(-11,-6) $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let A, B, be the centres of the two circles, Slope of the common tangent $ =-\frac{12}{5} $
$ \therefore $ Slope of AB is $ \tan \theta =-\frac{1}{-\frac{12}{5}}=\frac{5}{12} $ The point (1, -1) lies on the line AB and the points A and B are at a distance 13 from the point (1,-1)
$ \therefore $ Coordinates of A and B are $ (1\pm 13cos\theta ,-1\pm 13\sin \theta ), $ where $ \tan \theta =\frac{5}{12} $ i.e. $ ( 1\pm 13\frac{12}{13},-1\pm 13\frac{5}{13} ) $ or $ (1\pm 12,-1\pm 5) $ i.e., $ (13,4) $ and $ (-11,-6) $
BETA
