Question

please help!

A circle is inscribed in a square whose vertices have coordinates R(0, 4), S(6, 2), T(4, -4), and U(-2, -2). Find the equation of the circle.

-(x - 2)² + y² = 68
-(x - 2)² + y² = 10

Answer 1

Those aren't negative signs in front of the first terms, are they? (They shouldn't be.)

If you find the midpoint between two opposite vertices of the square (e.g., 2 corners that are diagonally across from one another) then that is the center of the square, hence, the center of the circle. So that gives you your (h,k) in the circle equation.

Answer 2

Then you just need the radius. Again, think about how the radius of the circle is related to the square.

You know the points for the 4 corners of the square, so from those points, how can you get the radius?