Identify the center and radius from the equation of the circle given below. x^2+y^2+121-20y=-10x

Center: (-5,10)

Radius: 2

Step-by-step explanation:

The equation of the circle in center-radius form is:

Where the point (h,k)  is the center of the circle and "r" is the radius.

Subtract 121 from both sides of the equation:

Add 10x to both sides:

Make two groups for variable "x" and variable "y":

Complete the square:

Add inside the parentheses of "x".

Add    inside the parentheses of "y".

Add and to the right side of the equation.

Then:

Rewriting, you get that the equation of the circle in center-radius form is:

You can observe that the radius of the circle is:

And the center is:

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

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step-by-step explanation: