Question

The circle $x^2+y^2=4x+8y+5$ interesects the line 3x - 4y = m at two distinct points if
(2010)

• A. -35 < m < 15
• B. 15 < m < 65
• C. 35 < m < 85
• D. -85 < m < -35

Answer 1

The correct option is A

-35 < m < 15

Circle $x^2+y^2-4x-8y-5=0$
Centre = (2, 4), Radius $=\sqrt{4+16+5}=5$
If circle is intersecting line 3x - 4y = m at two distinct points.
$\Rightarrow$ length of perpendicular from centre < radius
$\Rightarrow \frac{|6-16-m|}{5}<5\Rightarrow |10+m|<25$
$\Rightarrow$ -35 < m < 15.