Could you show me the steps on how to figure out the (h,k) radius?
You need to define your terms.
To find the radius (r) and center (h,k) of a circle given its equation in the form (x-h)^2 + (y-k)^2 = r^2, follow these steps:
Step 1: Identify the values of h and k.
The values h and k represent the x-coordinate and y-coordinate of the center of the circle, respectively. In the given equation, (x-h)^2 indicates that the x-coordinate of the center is h, and (y-k)^2 indicates that the y-coordinate of the center is k. Identify these values in the equation.
Step 2: Determine the radius.
The equation is in the form (x-h)^2 + (y-k)^2 = r^2, where r represents the radius of the circle. To find the radius, compare the given equation with the standard form and isolate r^2. For example, if the given equation is (x-2)^2 + (y+1)^2 = 25, then r^2 = 25. Therefore, the radius is the square root of 25, which is 5.
Step 3: Write the center and radius in the appropriate format.
Now that you have determined the values of h, k, and r, write the center as (h,k) and the radius as r. Using the previous example, the center is (2,-1) and the radius is 5. So, the (h,k) radius is (2,-1) with a radius of 5.