Yeah sorry I fixed it...
If you replace "m" with "y" it becomes the conic section which is a hyperbola having axes of symmetry at an angle about 5 degrees off the vertical. Any horizontal line (value of y or m) crosses it in two different places, giving two different values of x, while any vertical line (value of x) crosses it in two different places, giving two different values for y (or m).
I think what HallsofIvy is saying is that the fact that does not imply that x has to be -3 in any way. You can take different values of x and get different values of m or vice versa. The problem arbitrarily says to find m that satisfies the equation when x = -3. You found correctly that m = -1.5 or m = 1.