Question

The ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3).

How do i do this?

Answer 1

They want me to find the equation of the ellipses.

Answer 2

So y= (3,-3) and x = (5,-5) ?

Answer 3

you know what the center is right?

Answer 4

Zero right?

Answer 5

well actually it is \((0,0)\)

Answer 6

the general equation is \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\] where the center is \((h,k)\) but since your center is \((0,0)\) you know it is
\[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] so now you job is only to find \(a^2\) and \(b^2\)

Answer 7

\(a^2\) is easy to find
because of the orientation, you know that \(a\) is the larger of the two numbers, and since the vertices are \((-5,0)\) and \((5,0)\) you know \(a=5\) and so \(a^2=25\)

Answer 8

to find \(b^2\) compute \(5^2-3^2\)

Answer 9

ok. So 16?