SOLUTION: Determine the equation of the line through the center of the circle that is perpendicular to the diameter with endpoints at (4,2) and (4,-8). Write the answer in slope intercept fo

Algebra ->  Points-lines-and-rays -> SOLUTION: Determine the equation of the line through the center of the circle that is perpendicular to the diameter with endpoints at (4,2) and (4,-8). Write the answer in slope intercept fo      Log On


   

Question 944392: Determine the equation of the line through the center of the circle that is perpendicular to the diameter with endpoints at (4,2) and (4,-8). Write the answer in slope intercept form (y=mx+b)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use the diameter endpoints to determine the equation of the circle.
The size of radius is 5, and center is at x=4, y=%282%2B%28-8%29%29%2F2=-3.
Circle Equation, %28x-4%29%5E2%2B%28y-%28-3%29%29%5E2=25, or highlight%28%28x-4%29%5E2%2B%28y%2B3%29%5E2=25%29.


line through the center of the circle that is perpendicular to the diameter

The given diameter with the given two points is vertical. The slope for any line perpendicular to that diameter is 0. The line is also specified to need to contain the center of the circle, (4,-3).

The requested line is simply highlight%28y=-3%29;
in this case, x is unrestricted, m=0, and b=-3.
You could give the equation as y=0%2Ax-3.