Question

If the circle `x^2+y^2-4x-8y-5=0` intersects the line `3x-4y=m` at two distinct points, then find the values of `mdot`
A. `35 lt m lt 85`
B. `-85 lt m lt - 35`
C. `-35 lt m lt 15`
D. `15 lt m lt 65`

Answer 1

Correct Answer - C
The circle is
`x^(2)+y^(2)-4x-8y-5=0`
Its centre is `(2,4)` and radius is `sqrt(4+16+5)=5`
If the circle intersects the line `3x-4y=m` at two distinct points, then the length of the perpendicular from the centre is less than the radius, i.e.,
`(|6-16-m|)/(5) lt5`
`implies |10+m| lt25`
`implies 25 lt m +10lt25`
`implies -35ltmlt15`