Circle x2+y2−4x−8y−5=0 Centre =(2,4), Radius =4+16+5=5 If circle is intersecting line 3x−4y=m at two distinct points. ⇒ length of perpendicular from centre < radius ⇒5∣6−16−m∣<5 ⇒∣10+m∣<25 ⇒−25<m+10<25 ⇒−35<m<15.
The circle x2+y2=4x+8y+5 intersects the line 3x−4y=m at two distinct points if
Held on 30 Apr 2010 · Verified 6 Jul 2026.
−35<m<15
15<m<65
35<m<85
−85<m<−35
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