What is the radius of a circle with the equation x² + y² - 14x + 10y = 250?

Solution:

Given:

Equation of circle is x² + y² - 14x + 10y = 250

Grouping the terms having same variables and adding and subtracting 49 and 25 to the LHS to make the perfect square.

x² - 14x + 49 - 49 + y² + 10y + 25 - 25 = 250

So we get,

(x - 7)² - 49 + (y + 5)² - 25 = 250

(x - 7)² + (y + 5)² = 250 + 49 + 25

(x - 7)² + (y + 5)² = 324

The general equation of circle is (x - h)² + (y - k)² = r²

Where (h, k) are center of the circle and 'r' is the radius of the circle.

By Comparing (x - 7)² + (y + 5)² = 324 with the general equation, we get

r² = 324

r = √324

= 18

Therefore, the radius of the circle is 18.

---

What is the radius of a circle with the equation x² + y² - 14x + 10y = 250?

Summary:

The radius of a circle with the equation x² + y² - 14x + 10y = 250 is 18.