What is the radius of a circle with the equation x^2+y^2-14x+10=250

radius is 17

Step-by-step explanation:

Use "completing the square" to rewrite the given equation in standard form for a circle centered at (h, k) with radius r:

x^2+y^2-14x+10=250 becomes:

x^2 - 14x + y^2 = 240 after grouping x terms and  y terms separately.

Completing the square, once for x and once for y, results in:

x^2 - 14x + 49 - 49 + y^2 = 240.

Rewriting x^2 - 14x + 49 as the square of the binomial x - 7 results in:

(x - 7)^2 + y^2 = 289 = 17^2

From this we recognize that the center is at (7, 0) and the radius is 17.