Here are the answers to all the questions. I didn't check my answers FYI.
The standard equation of a circle:
(y-k)² + (x-h)² = R² (1), where R is the radius and h, k are the coordinates of the center.: C(h, k)
In the problem the coordinates of the center C(2,-1).
Replace in (1) h by 2 and k by -1:
(y+1)² + (x-2)² = 25
Answer:

Step-by-step explanation:
We are given that a line passes through (-2, 8) and has a slope of -5/2.
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope of this line, we can immediately plug it into the equation.
Replace m with -5/2.

Now we need to find b.
As the equation passes through the point (-2, 8), we can use its values to help solve for b.
Substitute -2 as x and 8 as y.

Multiply.
8 = 5 + b
Subtract 5 from both sides.
3 = b
Replace b with 3 in the equation.

Topic: finding the equation of the line (slope-intercept form)
See more: brainly.com/question/27959192
x^2 + 2 = 38
Subtract 2 from each side:
x^2 = 36
Take the square root of both sides:
x = √36
x = 6