ellipses: which one is centered at the origin and....

[KHoward0049]

I am so lost. I am looking at my choices for the answer, and all I am seeing is repeats.

QUESTION: Which of the following is the equation of an ellipse centered at the origin with major axis length to 50 and minor axis length equal to 26?

ANSWERS:

A) x^2 / 169 + y^2 / 625

B) x^2 / 676 + y^2 / 2500

C) x^2 / 26 + y^2 / 50

D) x^2 / 13 + y^2 / 25

I am getting A and D to be the same answer and B and C to be the same. I am getting the answer like B and C just the denominators flipped. Am I doing something wrong? Oh, and just so everyone knows, I am studying for my final exam. I have to try to get at least a 90.

 

[soroban]

Re: ellipses....

Hello, KHoward0049!

Think about what you said . . .

Which of the following is the equation of an ellipse centered at the origin
with major axis length to 50 and minor axis length equal to 26?

\(\displaystyle \L A)\;\frac{x^2}{169}\,+\,\frac{y^2}{625}\:=\:1\;\;\;\;B)\;\frac{x^2}{676}\, +\,\frac{y^2}{2500}\:=\:1\)

\(\displaystyle \L C)\;\frac{x^2}{26}\,+\,\frac{y^2}{50}\:=\:1\;\;\;\;D)\;\frac{x^2}{13}\,+\,\frac{y^2}{25}\:=\:1\)

I am getting A and D to be the same answer and B and C to be the same. ??

Then: \(\displaystyle \L\,169\,=\,13\,\) and \(\displaystyle \L\,625\,=\,25\) . . . right?

 

[skeeter]

an ellipse centered at the origin has the equation ...

\(\displaystyle \L \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

where 2a = length on one axis
2b = length of the other axis

of course, the title of "major" or "minor" axis depends on the relative sizes of a and b.

... so, what would you call the conic where a = b?

 

[KHoward0049]

Only one answer is correct, and I am not personally seeing the correct answer. I am gettting the answer:

. . .x^2 / 2500 + y^2 / 676

So what am I doing wrong? I am usually pretty good at solving these type of problems. I am not getting what they want.

 

[stapel]

So what am I doing wrong?

Dunno. Please reply showing your work, so we can see what you are doing.

Thank you.

Eliz.

 

[KHoward0049]

The major axis = A = 2500 or 50^2.
The minor axis = B= 676 or 26^2.
The major axis is the larger number making the major axis horizontal and the minor axis is vertical. The horizontal ellipse formula is x^2/a^2 + y^2/b^2.
I put it all into the formula and I am getting the answer I said above. I am not getting any of the choices that are being given.

 

[stapel]

You might want to review skeeter's earlier reply, spefically with respect to axis length.

Eliz.