SOLUTION: The center of a circle is at (2,-5), one point on the circle is (-4,2).Find the other end of the diameter through (-4,2).

Algebra ->  Circles -> SOLUTION: The center of a circle is at (2,-5), one point on the circle is (-4,2).Find the other end of the diameter through (-4,2).      Log On


   

Question 1030760: The center of a circle is at (2,-5), one point on the circle is (-4,2).Find the other end of the diameter through (-4,2).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
r%5E2=%28%28-4-2%29%5E2%2B%282-%28-5%29%29%5E2%29
r%5E2=%2836%2B49%29
r%5E2=%2885%29

%28x-2%29%5E2%2B%28y%2B5%29%5E2=85------but not really what you need.

The distance from center to any point on the circle is sqrt%2885%29.
The center, and the endpoints for any of the diameters of the circle, are collinear.

The line containing this diameter contains the points (2,-5) and (-4,2). Using point-slope form, the equation for this line is y%2B5=%28%282%2B5%29%2F%28-4-2%29%29%28x-2%29
y%2B5=-%287%2F8%29%28x-2%29
y=-%287%2F8%29x%2B14%2F8-5
y=-%287%2F8%29x%2B7%2F4-5......
upon further thinking, this approach seems more complicated than necessary.



The center (2,-5) is the MIDPOINT between the two endpoints for the diameter; and one endpoint is given to be (-4,2). The unknown endpoint is some ordered pair (x,y). Setup the midpoint formula for the circle's center and the two endpoints.

system%28%28x%2B%28-4%29%29%2F2=2%2C%28y%2B2%29%2F2=-5%29

system%28x-4=2%2A2%2Cy%2B2=-10%29

system%28x=8%2Cand%2Cy=-12%29

The other diameter's endpoint is (8,-12).