Please help! A circle with center C(4,8) has a radius 10. A. Verify that A(-2, 16) and B (12, 14) are points on this circle B. If M is the midpoint of AB, show that CM perpendicular AB I Do Not Understand? Help Please?

Question

mathmale · Answer

Yes?  What is your goal here?  Please always share the instructions for every problem you post.

anonymous · Answer

Assuming you want to find the equation:
(x - 4)^2 + (y- 8)^2 = 100.

mathmale · Answer

Yes.  My goals here are to remind DMJ to include the instructions with each problem posted, and to ask questions/give guidance towards helping him/her learn how to actually solve the problem himself/herself.

anonymous · Answer

Please help!
A circle with center C(4,8) has a radius 10.
A. Verify that A(-2, 16) and B (12, 14) are points on this circle
B. If M is the midpoint of AB, show that CM perpendicular AB
I Do Not Understand? Help Please?

anonymous · Answer

A. wants you to check to see if the pts are in the circle. Find the distance between the pt and the center, and see if it's 100.
1st point. Yes.
2nd point. Yes also.
B. Find the equation of the line that has pts A and B in it. Then find the equation of the line that has pts C and M in it. Compare their slopes (they should be inverses).

anonymous · Answer

A simpler way to do A is that you find the difference in the x values and the y values, and then add their squares together. If it equals to 100, the pt is in the circle. If not, then it's not.

mathmale · Answer

I'd suggest starting the with the standard equation of a circle with center (h,k) and radius r.  That equation is $$(x-h)^2+(y-k)^2=r^2$$

mathmale · Answer

In the very first part of this problem, you are given the center (4,8) and the radius 10.  that means that h=4, k=8 and r=10.

All you need to do is to substitute these values into the equation I gave you, above.