# Thread: Equations of the circle, midpoints and so on.

1. ## Equations of the circle, midpoints and so on.

Hey,
I'm pretty ok at maths however I really get stuck on the whole circle problems and would appreciate some help

1. Part 1 - Find the mid-point, C, of AB where A is (1,8) and B is (3,14) respectively.

Part 2 - Find the distance between AC

Part 3 - Find the equation of the circle which has AB as diameter.

Thanks a lot

2. midpoint

$\displaystyle \frac{1+3}{2}, \frac{14+8}{2}$

3. Ok so midpoint is 2,11 should have said I already got that but that's the easy bit.

4. part 2

distance formula

$\displaystyle \sqrt{(2-1)^2 +(11-8)^2} =$

5. So thats Square Root of 10 overall which is 3.16227766..and so on.
Now the 3rd part

6. The distance between A and C, or the length of the line segment AC, is calculated as:

$\displaystyle \sqrt{(2-1)^2 + (11-8)^2}$

The circle with AB as diameter has center C, and its radius is the length of AC. The equation for a circle with center (h, k) and radius r is $\displaystyle (x-h)^2 + (y-k)^2 = r^2$. Just plug in the numbers; you've got all of them now.

7. Does that mean I use the vales of C for h,k so it would be as follows?

$\displaystyle (x-2)^2 + (y-11)^2 = r^2$

8. Yes, you use the coordinates of C for h and k.