Question

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

• 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 $=\sqrt{4+16+5}=5$

lf circle is intersecting line $3x-4y=m$
at two distinct points.

Length of perpendicular from center $<$ radius

$=\frac{|6-16-m|}{5}<5$

$=|10+m|<25$

$=-25<m+10<25$

$=-35<m<15$.