Question

Find the radius of the circle with equation x^2 + y^2 - 10x - 16y + 53 = 0.

Answer 1

radius = 10.5 units

Explanation:

Equation of a circle is given by

x² + y² + 2gx + 2fy + c = 0

To find the radius of the circle we use the formula

`r = \sqrt{ {g}^(2) + {f}^(2) - c }`

where g and f is the center of the circle

From the question

x² + y² - 10x - 16y + 53 = 0

Comparing with the general equation above we have

2g = - 10 2f = - 16

g = - 5 f = - 8

c = 53

Substitute the values into the above formula

That's

`r = \sqrt{ ({ - 10})^(2) + ( { - 8})^(2) - 53 }`

`r = √(100 + 64 - 53)`

`r = √(111)`

We have the final answer as

radius = 10.5 units

Hope this helps you