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

Question

anonymous · Answer

$$vertices (0,\pm7)  foci  (0,\pm \sqrt{33)}$$

turingtest · Answer

This equation is a vertical ellipse so we are working with something like$${x \over a^2}+{(y-k)^2\over b^2}=1$$Zarkon please get us started, I'm relearning this as I'm teaching it, how do we get a and b again?

zarkon · Answer

$$b^2=7^2$$

zarkon · Answer

k=0

zarkon · Answer

$$a^2=b^2-c^2$$

where c is the foci

turingtest · Answer

oh right, because it is in the center.
so we have$${x^2\over a^2}+{y^2\over b^2}=1$$and $$a^2=b^2-c^2$$as Zarkon said $$b^2=7^2$$and we know what c is, so we can get a.

turingtest · Answer

Unfortunately you will have to memorize some equations. I had forgotten the second one above.
So what is $$c^2$$??? (as said above c is the foci)

zarkon · Answer

you can derive the formulas ...just by memorizing the definition of the ellipse ...gotta go eat...enjoy

turingtest · Answer

Yes I did that once, using the geometry of a string. I was very proud of myself, but have forgotten most of it now.

turingtest · Answer

a string attatched to two pins I mean

anonymous · Answer

lol thats what all my teachers say is that theyve done circles in geometry but dont know what im doing in algebra 2. it doesnt make sense when their supposed to be the teacher... thanks for all your help guys.

turingtest · Answer

so did you get a? we almost have it here I remember enough to help you if you are not sick of it yet.

anonymous · Answer

you explained the part that i get stuck on.

turingtest · Answer

right on, I'll study up on ellipses for you if you have more questions. good luck!

anonymous · Answer

thanks so much... your more help then the teachers i have. :) enjoy your night.