What is the radius of a circle with the equation x2 + y2 - 14x + 10y = 250? A) 9 units B) 12 units C) 15 units D) 18 units

D

Step-by-step explanation:

To find the radius of the circle with equation x2 + y2 - 14x + 10y = 250, convert the equation into vertex-form (x - h) ² + (y-k) ² = r². Convert by completing the square for x² - 14x and y² + 10y.

Complete the square by dividing each term - 14x and 10y in two. Then square each.

-14/2 = - 7 and - 7² = 49

10/2 = 5 and 5² = 25

The equation becomes x² - 14x + 49 + y² + 10y + 25 = 250 + 49 + 25.

We simplify the equation into (x-7) ² + (y + 5) ² = 324.

324 is the value of radius squared. Take the square root to find the radius.

√324 = 18

The radius is 18 units.