Question

Write the equation of an ellipse with vertices (0, 5) and (0, -5) and co-vertices (2, 0) and (-2, 0).

Answer 1

`(x^2)/(4) +(y^2)/(25) =1`

Explanation:

From a sketch of the given coordinates, you notice that the ellipse has its center at (0,0) i.e origin

It is a vertical ellipse centered at (0,0),

The major axis has its coordinates at (0,a) = (0,5) and (0,-a) =(0,-5)

The minor axis has it coordinates at (0,b)=(0,-2) and (0,2)

Here a>b

The length of major axis is 2a = 2*5= 10

The length of minor axis is 2b= 2*2=4

Equation is given by

`(x^2)/(b^2) +(y^2)/(a^2) =1\\\\\\(x^2)/(2^2) +(y^2)/(5^2) =1\\`