Question

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

Answer 1

Answer:

$\frac{x^2}{4} +\frac{y^2}{25} =1$

Step-by-step 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

$\frac{x^2}{b^2} +\frac{y^2}{a^2} =1\\\\\\\frac{x^2}{2^2} +\frac{y^2}{5^2} =1$