Question

Write the equation of a circle whose center is (-2,3) and which has a radius of 4 .

Answer 1

`{(x + 2)}^(2) + {(y - 3)}^(2) = 16`

Answer 2

The equation of the circle is
`(x + 2)^2 + (y - 3)^2 = 16`

Explanation:

The equation of a circle with center(h,k) and radius(r) is given by the formula:

`\sf (x - h)^2 + (y - k)^2 = r^2`

In this case, the center is (-2, 3) and the radius is 4.

Plug these values into the equation:

`\sf (x - (-2))^2 + (y - 3)^2 = 4^2`

`\sf (x + 2)^2 + (y - 3)^2 = 16`

So, the equation of the circle is:

`\sf (x + 2)^2 + (y - 3)^2 = 16`