Question

24. Identify the center and radius of the circle given the equation (x +15)2 + (7 - 9)2 = 25 .

a. Center: (-15, 9), Radius: 5
b. Center: (15, -9), Radius: 25
c. Center: (-15, -9) Radius: 5
d. Center: (15,9) Radius: 25

Answer 1

a. Center: (-15, 9), Radius: 5

Explanation:

Equation of a circle:

The equation of a circle of center
`(x_0, y_0)` and radius r is given by:

`(x - x_0)^2 + (y - y_0)^2 = r^2`

In this question, we have that:

`(x + 15)^2 + (y - 9)^2 = 25`

Comparing both equations:

`x - x_0 = x + 15`

`x_0 = -15`

And

`y - y_0 = y - 9`

`y_0 = 9`

The center is
`(-15,9)`.

For the radius:

`r^2 = 25`

`r = √(25) = 5`

The correct answer is given by option a.