Question

Write the equation in standard form for the circle with center (–
6,0) and radius 5.

Answer 1

`(x - 6)^2 + y^2 = 25`

Explanation:

The standard form of a circle is
`(x - x_1)^2 + (y - y_1)^2 = \text{R}^2`, where
`(x_1\text{, }y_1)` is the center point of the circle, and
`\text{R}` is the circle's radius.

We're given the center of our circle is (6, 0) and its radius is 5, therefore, the circle's equation in standard form is:

`(x - 6)^2 + (y - 0)^2 = 5^2\\\to (x - 6)^2 + y^2 = 25`

Answer 2

(x - 6)² + y² = 25

Explanation:

the equation of a circle in standard form is

(x - h)² +(y - h)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (6, 0 ) and r = 5 , then

(x - 6)² + (y - 0)² = 5² , that is

(x - 6)² + y² = 25