Question

Consider the circle with an equation in standard form: ( x – 4)² + ( y + 2)² = 36 . Explain in 2-3 sentences or explain the steps used to find the radius and the center.

Answer 1

Answer:

The center of this circle is found at (4, -2) and the radius is 6.

Step-by-step explanation:

The equation for a circle in standard for is  ( x – h)² + ( y - k)² = r². In this equation, (h, k) is the center of the circle and r is the radius.

From the given equation, ( x – 4)² + ( y + 2)² = 36, h is already subtracted from x, so h = 4, but the k is not subtracted, so (y + 2) = [y - (-2)], and we see that k is -2. Therefore, the center of the circle is (4, -2) and 36 = r². By taking the square root of 36, we find that r = 6.

The center of this circle is found at (4, -2) and the radius is 6.