Answer:
Explanation:
To find the equation of a circle, we need to know the center of the circle and its radius.
The center of the circle is given as (-1, 3), and the circle passes through the point (3, 7).
We can use the distance formula to find the radius of the circle:
r = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(3 - (-1))^2 + (7 - 3)^2]
= √[(4)^2 + (4)^2]
= √32
So the radius of the circle is √32.
Now, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle, and r is the radius.
Plugging in the values we found, we get:
(x - (-1))^2 + (y - 3)^2 = (√32)^2
Simplifying this equation, we get:
(x + 1)^2 + (y - 3)^2 = 32
Therefore, the equation of the circle with the center at (-1, 3) and passing through the point (3, 7) is (x + 1)^2 + (y - 3)^2 = 32.