Question

What write the equation of a circle that has a diameter of 16 units and it’s center is at (3,-5)?

Answer 1

(x - 3)^2 + (y + 5)^2 = 64

Explanation:

We can find the equation of the circle in standard form, which is

`(x-h)^2+(y-k)^2=r^2`, where

• (h, k) is the center,
• and r is the radius

Step 1: We see that the center is (3, -5). Thus, in the formula, 3 becomes -3 for h and -5 becomes 5 for k since -(-5) becomes 5.

Step 2: We know that the diameter is equal to 2 * the radius. Thus, if we divide the diameter of 16 by 2, we see that the radius of the circle is 8 units

Step 3: Now, we can plug everything into the equation and simplify:

(x - 3)^2 + (y + 5)^2 = 8^2

(x - 3)^2 + (y + 5)^2 = 64