Question

Which of the following is the equation of an ellipse centered at (4,-1) having a horizontal minor axis of length 14 and a major axis of length 20?

Answer 1

If you have an ellipse centered at (4,-1) that means it will be of the form
\[\frac{(x-4)^2}{a^2}+\frac{(y+1)^2}{b^2}=1\]

Think of the - and + in the numerator as the translation from the simple case where the ellipse is centered on (0,0).

Answer 2

That rules out the first possibility.

If a>b, the ellipse has a horizontal major axis. If a < b, the ellipse has a vertical major axis. If a = b, you've got that special ellipse known as a circle. We've got a horizontal minor axis which means we have a vertical major axis and a<b.

Answer 3

That rules out the third possibility. Still have two to choose from. Because we've got a major axis of 20, we've got a semimajor axis of 10 (center to the vertice) and similarly, our minor axis of 14 -> semiminor axis of 7. The nice thing is that the values are a and b! So we know that our equation is \[\frac{(x-4)^2}{7^2}+\frac{(y+1)^2}{10^2}=1\]

Answer 4

We know that a = 7, not 10, because the ellipse is vertical -> a < b.

Answer 5

I've always hated ellipse problems, but @hero asked me to help, so I did! :-)

Answer 6

thank you soooo much!!! @whpalmer4 i understand it so much better now :) can you help me with one more problem!? youre great :)

Answer 7

Sure, ask away. My kid came home and wanted to show me his haul from the Lego store, sorry for not responding...

Answer 8

aw how cute, i got it actually so no need for help anymore :) thanks anyway!

Answer 9

Even better! Now go show you best friend how to do ellipse problems. That's the secret to really solidifying your knowledge — teach someone else.