Geometry and finding equations

Question

Find and equation of the circle that has center (-3,4) and passes through (2,5)

Answer 1

The equation of a circle in a plane has only 2 parameters (numbers we need to solve for): the coordinates of the center and the radius length. If we know those numbers, we can write the equation in this form:

(x - h)² + (y - k)² = r² where the center is at (h , k) and the radius length is r. x and y will remain as variables.

We can plug in the coordinates for the center right away: (x + 3)² + (y - 4)² = r²

Now we just need r, which we can find by using distance formula, since we know the point (2,5) lies on the circle. We calculate the distance between (2,5) and (-3,4) (the center) and that will be r:

r² = (2 - -3)² + (5 - 4)² = 26. So r = √26 , and the equation is (x + 3)² + (y - 4)² = 26

Answer 2

(x + 3)² + (y - 4)² = r²;

Because point (2,5) belong to circle we have ((2 + 3)² + (5 - 4)² = r²; r² = 26

So, equation of circle: (x + 3)² + (y - 4)² = 26.