Write the equation of the circle in standard form that has the following:
Center (-5,7) and Radius = 4
The standard form of the equation of a circle is given by:
(x - h)^2 + (y - k)^2 = r^2,
where (h, k) represents the center of the circle and r represents the radius.
In this case, the center is (-5, 7) and the radius is 4. Plugging these values into the equation gives:
(x - (-5))^2 + (y - 7)^2 = 4^2
Simplifying:
(x + 5)^2 + (y - 7)^2 = 16
Therefore, the equation of the circle in standard form is:
(x + 5)^2 + (y - 7)^2 = 16.
The general equation of a circle in standard form is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
Given that the center is (-5,7) and the radius is 4, we can substitute these values into the equation:
(x - (-5))^2 + (y - 7)^2 = 4^2
Simplifying,
(x + 5)^2 + (y - 7)^2 = 16
Therefore, the equation of the circle in standard form is (x + 5)^2 + (y - 7)^2 = 16.