Find the equation of the circle that passes through the
origin and has its center at (-3,-4).
The equation of a circle with center (h,k) and radius r is
(x - h)² + (y - k)² = r²
We do not know the radius r, but we do know h and k,
(h, k) = (-3, -4), so we have
(x + 3)² + (y + 4)² = r²
Now since we are told that the circle passes through the
origin, then we can substitute (x, y) = (0, 0)
(x + 3)² + (y + 4)² = r²
(0 + 3)² + (0 + 4)² = r²
3² + 4² = r²
9 + 16 = r²
25 = r²
5 = r
So the equation is
(x + 3)² + (y + 4)² = 5²
(x + 3)² + (y + 4)² = 25
Your teacher may want you to multiply that out and get
x² + y² + 6x + 8y = 0
Edwin
