SOLUTION: Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0). My book doesn't show me

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0). My book doesn't show me       Log On


   

Question 74446This question is from textbook Algebra 2
: Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).
My book doesn't show me how to write the equation with the major and minor axis points. Can someone help me? Thanks! This question is from textbook Algebra 2

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
MY ORIGINAL ANSWER TO THIS QUESTION HAD THE MAJOR AND MINOR AXES REVERSED. THIS HAS BEEN CORRECTED. I APOLOGIZE FOR THE ERROR.

A general equation for an ellipse centered at (h,k), with the major axis parallel to the y axis is:

%28%28%28x-h%29%5E2%29%2Fb%5E2%29%2B%28%28%28y-k%29%5E2%29%2Fa%5E2%29=1

For your case:
the ellipse is centered at (1,0),, the intersection of the major and minor axes
the length of the major axis (a) is 12,, the distance between (1,6) and (1,-6)
the length of the minor axis (b) is 8,, the distance between (5,0) and (-3,0)

So the equation is:

%28%28%28x-1%29%5E2%29%2F64%29%2B%28%28y%5E2%29%2F144%29=1