Final answer:
To write the equation of a circle, we need the coordinates of the center and the radius. The center of the circle is given as (-4,3), and a point on the circle is (-6,1).
Step-by-step explanation:
To write the equation of a circle, we need the coordinates of the center and the radius. The center of the circle is given as (-4,3), and a point on the circle is (-6,1).
We can use the distance formula to find the radius of the circle, which is the distance between the center and the point on the circle. The distance formula is:
d = √[(x2 - x1)² + (y2 - y1)²]
Using the given coordinates, we substitute x1 = -4, y1 = 3, x2 = -6, and y2 = 1 into the distance formula and calculate the radius:
d = √[(-6 - (-4))² + (1 - 3)²]
d = √[(-2)² + (-2)²]
d = √[4 + 4]
d = √8
So, the radius of the circle is √8. Now we can use the center and the radius to write the equation of the circle in the form (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius:
(x - (-4))² + (y - 3)² = (√8)²
(x + 4)² + (y - 3)² = 8