Question

Score for Question 2: ___ of 5 points) 2. Write the equation of the circle in general form. Show your work.

Answer 1

`x^2 + y^2 + 2x - 2y - 7 = 0`

Explanation:

Given

See attachment for circle

Required

The circle equation

First, we get the radius of the circle.

From the attachment, we have:

`r = 3`

Next, the center of the circle

`(h,k) = (-1,1)`

The equation of the circle is:

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

This gives:

`(x - -1)^2 + (y - 1)^2 = 3^2`

`(x +1)^2 + (y - 1)^2 = 3^2`

Expand

`x^2 + 2x + 1 + y^2 - 2y + 1 = 9`

Collect like terms

`x^2 + y^2 + 2x - 2y + 1 + 1 - 9 = 0`

`x^2 + y^2 + 2x - 2y - 7 = 0`

Hence, the equation in general form is:

`x^2 + y^2 + 2x - 2y - 7 = 0`