maths
posted by Anonymous on .
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+(y5)²=r² ??
Please help!

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
(x7)^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