Identify the center and radius for circle (x-a)^2+(y+b)^2=m

Question

Also,

Write an equation for the circle that's diameter has end points (-5,2) and (10,10)

Answer 1

This equation is already in the proper form to reveal that the vertex is at (a,b) and the radius is the square root of m.

 

To write the equation for the circle having the stated diameter endpoints, first use the distance formula to find the length of the diameter; half of that is the radius, r.

 

Then take the average of the x values of the endpoints and the average of the y values of the endpoints, to get the (a,b) coordinates of the center, the midpoint of the diameter.

 

Now you can put these numbers into the general equation: (x-a)²+(y-b)² = r² and you'll have answered this second question.