Question

1) Circle centre (7,-2) passes through (-2,10). Calculate radius and find equation of circle.

2) AB is diameter of circle A(9,5) B(-1,-7). Find equation of circle mid point.
I know i have to use the eqn (x1+x2)/2 and (y1+y2)/2

3) Find the equation of circle with centre (-8,5). Which has y axis as tangent. Find equation of circle.
?? (x+8)²+(y-5)²=r² ??

Please help!

Answer 1

1)
The radius is the distance from the center , (7,-2), to the point (-2,10)
I bet you know the distance formula:
r^2 = (X2 - X1)^2 + (Y2 - Y1)^2
Then
(x-7)^2 +(y+2)^2 = r^2

2)
Yes, the center is at the average of those two points on opposite sides of the circle.
I think it is also asking for the equation of the circle.
Once you have found the center, you can find the equation the same way you found it in #1 but for r^2 use the distance^2 from center to one of those given points.

3)
The y coordinate of the center is 5.
Therefore the tangent to the y axis will be 8 units to the right of the center and at y = 5. (Draw a sketch) In other words at (0,5)
The radius is therefore 8 and r^2 = 64