Question

Find the standard equation for the ellipse using the characterstics given vertices: (0, PM7) foci (0, Sqrt PM 33)

Answer 1

Standard form of the ellipse:

x^2/a^2 + y^2/b^2 = 1

and/or

x^2/b^2 + y^2/a^2 = 1

since the focii and vertices are at the (0, k) we use:

x^2/b + y^2/a = 1

c=foci = sqrt(33)

a = 7

c^2 = a^2 - b^2
33 = 49 - b^2
b=4

So equation is:

x^2/4^2 + y^2/7^2 = 1

x^2/16 + y^2/49 = 1

Answer 2

Third line in the message above should be:

x^2/b^2 + y^2/a^2 = 1

Answer 3

thanks so much again.