Write an equation of an ellipse in standard form with the center at the origin and a height of 4 units and width of 5 units.

The standard form of equation of an ellipse is in the form:

[(x – h)^2] / a^2 + [(y – k)^2] / b^2 = 1

Where, h and k are the center points, and a and b are one half the length of the major and minor axis.

Since height is 4 units and width is 5 units, therefore:

a = 5 / 2 = 2.5

b = 4 / 2 = 2

and h = k = 0 (at the origin)

The standard equation then becomes:

x^2 / (2.5)^2 + y^2 / 2^2 = 1

x^2 / 6.25 + y^2 / 4 =1

8+10

step-by-step explanation:

you multiply 4 by 2 and 5 by 2