Circle And System Of Circles Question 313
Question: Circle $ x^{2}+y^{2}-4x-8y-5=0 $ will intersect the line $ 3x-4y=m $ in two distinct points, if
Options:
A) $ -10<m<5 $
B) $ 9<m<20 $
C) $ -35<m<15 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Radius of given circle > Perpendicular distance from the centre of circle to the given line.
$ \Rightarrow \sqrt{4+16+5}>\frac{3(2)-4(4)-m}{\sqrt{9+16}} $
$ \Rightarrow \pm 25>-10-m\Rightarrow m+10>\pm 25 $
$ \Rightarrow -35<m<15 $ .
BETA
