Question

Circle P is graphed in the coordinate plane with center (-4, 7). Circle P contains the point (-1,9). What is an equation of circle P?

Answer 1

(x+4)² + (y -7)²=13

1) Since Circle P has the center (-4,7) then we can write out

(x-a)² + (y-b) = r² Plugging into a, and b the center coordinates we have

(x+4)² + (y +7)² = r²

2) Since the point (-1,9) belongs to that circle we can plug this point and find out the radius length:

(x+4)² + (y -7)² = r²

(-1+4)² + (9-7)² =r²

3² + 2² = r²

9 +4 = r² flip into the usual form

r² =13

r =√13

Note that since a point is made up of (x, y) coordinates we could do that

2.2) Now we can write out the answer.

3) The equation of that circle is:

(x+4)² + (y -7)²=13