determine the equation of the ellipse that is centered at (0,0), passes through the point (2,1) and whose minor axis is 4

Question

Can I get the step by step procedure? Thank you so much.

Answer 1

Equation has the form x² / a²  + y² / b² = 1

 

Length of minor axis = 2b = 4   So, b = 2

 

So, we have x² / a² + y² / 4 = 1

 

Since (2,1) is on the graph, 4 / a² + 1/4 = 1

 

                                                  4 / a² = 3/4

 

                                                     3a² = 16

 

                                                       a² = 16/3

 

Equation:  x² / (16/3) + y² / 4 = 1

 

Simplify:  3x² / 16 + y² / 4 = 1

 

         or  3x² + 4y² = 16