and
do not intersect.

Find possible range values for m.

Hey there mate :)

As per question, two equations are given.

We have to find the range of possible values of m so that both equations do not intersect.

If they intersect, both equations have to be satisfied by the same pair of (x,y) values.

We can then write :-

This is an equation of a line that passes through point (1,-1) and has a slope of m.

We can then rearrange the other equation as :-

This is the equation of a circle with radius and center at (2,1)

Then, we have m values where :-

1. Line intersects circle at two points

2. Line is tangent to circle at one point.

3. Line does not intersect the circle.

The interval of m where m does not intersect the circle will be between the two values of m where the line is a tangent to the circle, which happens at two points with different values of m.