Circle-And-System-Of-Circles Question 378
Question: If $ 5x-12y+10=0 $ and $ 12y-5x+16=0 $ are two tangents to a circle, then the radius of the circle is
[EAMCET 2003]
Options:
A) $ 20r^{2} $
B) $ 52r^{2} $
C) $ \frac{52}{9}r^{2} $
D) $ \frac{20}{9}r^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Equation of line is $ 3x-2y=k $ …… (i) Circle is $ x^{2}+y^{2}=4r^{2} $ ….. (ii) Equation of line can be written as $ y=\frac{3}{2}x-\frac{k}{2} $ Here, $ c=-\frac{k}{2},,m=\frac{3}{2} $ Now the line will meet the circle at one point, if $ c=\pm a\sqrt{1+m^{2}} $ $ =\frac{-k}{2}=\pm (2r),\sqrt{1+{{( \frac{3}{2} )}^{2}}} $ {From (ii), a = 2r} $ =\frac{k^{2}}{4}=4r^{2}\times \frac{13}{4} $ ,
$ \therefore $ $ k^{2}=52r^{2}. $
BETA
