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

**Solution:**

Given:

Equation of circle is x^{2} + y^{2} - 14x + 10y = 250

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

x^{2} - 14x + 49 - 49 + y^{2} + 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} = r^{2}**

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**

r^{2 }= 324

r = √324

= 18

**Therefore, the radius of the circle is 18.**

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

**Summary:**

The radius of a circle with the equation x^{2} + y^{2} - 14x + 10y = 250 is 18.