equation of circle?

Question

Find the equation of the circle centered at (h,k) = (-4,-2) and passing through the point (-1,2)

Answer 1

The equation of a circle comes in this standard form:
(x - h)² + (y - k)² = r², where r is the radius and (h, k) is the center.

In your example:
(x + 4)² + (y + 2)² = r²

The problem now is to find the value of r. This can be done by plugging in the values of a point on the circle, and solving for r. Or it can be done by discovering the length of the radius directly through the distance formula, using the point on the cirlce and the center as the endpoints of a segment.

The horizontal distance between point and center is 3. The vertical distance is 4. This gives an overall distance, via the Pythagorean Theorem, of 5. So, r = 5

Conversely, by solving via a point on the circle.
(x + 4)² + (y + 2)² = r²
(-1 + 4)² + (2 + 2)² = r²
(3)² + (4)² = r²
9 + 16 = r²
25 = r²; r = 5

Either way,
(x + 4)² + (y + 2)² = 5² = 25

Answer 2

eq of circle is (x-h)^2 + (y-k)^2 = r^2

(-1+4)^2 + (2+2)^2 = r^2
3^2 + 4^2 = r^2; r=5

(x+4)^2 + (y+2)^2 = 25

Answer 3

(x+4)^2 + (y+2)^2 = r^2
(-1+4)^2 + (2+2)^2 = r^2
3^2 + 4^2 = r^2

Should look familiar to you. r = 5

Equation: (x+4)^2 + (y+2)^2 = 25