Circle And System Of Circles Question 108
Question: If the lines $ 3x-4y+4=0 $ and $ 6x-8y-7=0 $ are tangents to a circle, then the radius of the circle is
[IIT 1984; MP PET 1994, 2002; RPET 1995, 97; Kurukshetra CEE 1998]
Options:
3/2
3/4
C) 1/10
D) 1/20
Show Answer
Answer:
Correct Answer: B
Solution:
The diameter of the circle is the perpendicular distance between the parallel lines (tangents) $ 3x-4y+4=0 $ and $ 3x-4y-\frac{7}{2}=0 $ and so it is equal to $ \frac{4}{\sqrt{9+16}}+\frac{7/2}{\sqrt{9+16}}=\frac{3}{2} $ .
Hence radius is $ \frac{3}{4} $ .
BETA
