Question

Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1

Answer 1

You should memorize the graphing formula for an ellipse, which is\[\frac{ (x-h)^2 }{ a^2 }+\frac{ (y-k)^2 }{ b^2 }=1 \] for a horizontal
or flip the a squared and b squared
And you should know what each of these variables means.
Your center is at (h,k), the major axis is 2a for a horizontal and minor is 2b, or for a vertical it is 2b for major and 2a for minor.
You also need the formula a^2-b^2=c^2, and c is the distance from center to focus.

so your problem is \[\frac{ x^2 }{ 100}+\frac{ y^2 }{ 36 } =1\]
They have already put it in graphing form, you just need to identify and then solve for variables. There is nothing on the tops of your fractions, meaning that both h and k are 0, and your center is at (0,0). Then, set a^2=100 and solve for a (10). Set 36=b^2, solve and get b=6
Your major vertices then are 10 left and right of your center (at (10,0) and (-10,0)) and the minor vertices are 6 above and below (at (0,-6) and (0, 6)

Use the a^2-b^2=c^2 formula for solve for c, you should get 8. Your foci go in the same direction as the major axis, so they are 8 left and right of the center at (-8,0) and (8,0)

I hope that helps! Ps, if you're not sure what I'm referring to as major and minor axis, foci etc, google a picture of a diagram of an ellipse

Answer 2

This was a great explanation thanks