maths
posted by Anonymous
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!

Damon
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
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