SOLUTION: I need help graphing an example of the equations of a hyperbola with an ellipse that share the vertices & center. Thanks a lot.

Algebra ->  Graphs -> SOLUTION: I need help graphing an example of the equations of a hyperbola with an ellipse that share the vertices & center. Thanks a lot.       Log On


   

Question 1079298: I need help graphing an example of the equations of a hyperbola with an ellipse that share the vertices & center. Thanks a lot.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

There are two cases.

Case 1.  If the hyperbola has equation %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1,

then for p < a,  any ellipse whose equation is%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fp%5E2=1
will share the vertices (h+a,k) and (h-a,k) and the center (h,k).

Case 2.  If the hyperbola has equation %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1,

then for p < a,  any ellipse whose equation is%28y-k%29%5E2%2Fa%5E2%2B%28x-h%29%5E2%2Fp%5E2=1
will share the vertices (h,k+a) and (h,k-a) and the center (h,k). 

Example and graph for case 1.

%28x-2%29%5E2%2F3%5E2-%28y%2B3%29%5E2%2F4%5E2=1 <-- hyperbola
%28x-2%29%5E2%2F3%5E2%2B%28y%2B3%29%5E2%2F2%5E2=1 <-- ellipse



Example and graph for case 2.

%28y-3%29%5E2%2F5%5E2-%28x-2%29%5E2%2F2%5E2=1 <-- hyperbola
%28y-3%29%5E2%2F5%5E2%2B%28x-2%29%5E2%2F2%5E2=1 <-- ellipse



Edwin