What is the center and radius of a circle with the given equation?
x^2 + y^2 – 4x + 10y = 7
To find the center and radius of a circle from its equation, we need to first manipulate the equation into the standard form:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
To do this, we need to complete the square for both the x and y terms:
x^2 - 4x + y^2 + 10y = 7
(x^2 - 4x + 4) + (y^2 + 10y + 25) = 7 + 4 + 25
(x - 2)^2 + (y + 5)^2 = 36
Now we can see that the center of the circle is (2, -5) and the radius is sqrt(36) = 6. Therefore, the center of the circle is (2, -5) and the radius is 6.