Question

Paula wants to know the center and radius of the circle described by the equation below:

x²+y²-2x+6y=15 What is a correct step in order for her to determine the center and radius?

Answer 1

To determine the center and radius of the circle, rearrange the equation to standard form, identify the values of h and k, and calculate the radius using a point on the circle.

Step-by-step explanation:

To determine the center and radius of the circle described by the equation x²+y²-2x+6y=15, Paula can follow these steps:

1. Rearrange the equation to the standard form of a circle equation (x-h)² + (y-k)² = r².
2. Identify the values of h and k, which represent the coordinates of the center of the circle.
3. Calculate the radius (r) using the equation r = sqrt((h-h')² + (k-k')²) where (h', k') are the coordinates of any point on the circle.