Question

The vertices on the major axis of an ellipse are the points (6, 12) and (−6, −12). The foci are the points (?

Answer 1

First, have you tried drawing this ellipse? You can often tell a lot about a geometric figure (such as an ellipse) by drawing it. Where does the center of the ellipse appear to be? What are the coordinates of the center?

And last, but most important, what's the most general equation of an ellipse centered at the point (h,k)?

Answer 2

I tried but it's really hard
Its due in a couple minutes could you please help me?

Answer 3

please someone help

Answer 4

So sorry you (and by implication, I) have to do this problem under pressure. It's not a difficult problem, really, but there's background material you'll need to understand what to do here.

Are you familiar with the terms "major axis," "minor axis," "standard equation of an ellipse with center at (0,0)" ?

Answer 5

Please see the example illustrated in this web page:

https://www.google.com/search?q=ellipse+equation&rlz=1C1CHFX_enUS461US461&espv=210&es_sm=122&tbm=isch&imgil=sukkSNL8fzM6bM%253A%253Bhttps%253A%252F%252Fencrypted-tbn0.gstatic.com%252Fimages%253Fq%253Dtbn%253AANd9GcTbuMJFv3uapo-Gx-No3RkGyvCsicfxSYczaSPkaFM3VgsAMb-9%253B640%253B480%253BKsRdNDqkC3xHKM%253Bhttp%25253A%25252F%25252Fwww.algebra.com%25252Falgebra%25252Fhomework%25252Fequations%25252FTHEO-20100329.lesson&source=iu&usg=__dVgnMu7CksNgp_N05tXWxI51S-I%3D&sa=X&ei=mbsQU8ayBcqwoQS-z4CQAw&ved=0CC4Q9QEwAQ&biw=1360&bih=673#facrc=_&imgdii=_&imgrc=sukkSNL8fzM6bM%253A%3BKsRdNDqkC3xHKM%3Bhttp%253A%252F%252Ftheo.x10hosting.com%252Fexamples%252FEllipse%252FEllipse7.jpg%3Bhttp%253A%252F%252Fwww.algebra.com%252Falgebra%252Fhomework%252Fequations%252FTHEO-20100329.lesson%3B640%3B480

The ellipse you're working has a graph very similar.

Have you seen those labels a, b, c before?

Answer 6

In the illustration, " a " is the distance from the center of the ellipse to a vertex: " b " is the distance from the center along the "minor axis" to the graph; and c is the distance from the center to a focus. For an ellipse, b^2=a^2-c^2.

Answer 7

If you'd like to finish this problem, even though you may no longer be able to earn credit for it, let me know. I'd be happy to help you further.

Answer 8

please help if you can

Answer 9

Carolyn, much depends on whether you've included all given info when posting this question. You state that the vertices of this ellipse are (-6,12) and (6,12). That info alone is insufficient to calculate a numeric answer to the question: Find the points that represent the foci of this ellipse. Would you mind checking this out, if it's still possible?

Answer 10

Supposing that what you've typed out really is all the info that you have.
Then you could write the general equation of an ellipse with center at (h,k):\[\frac{ (x-h)^2 }{ a^2}+\frac{ (y-k)^{2} }{ b ^{2} }=1\]
which, if the center is at (0,12) as it is in the homework problem you've posted, becomes
\[\frac{ (x-0)^2 }{a^2 }+\frac{ (y-12)^2 }{ b ^{?} }=1\]

Answer 11

Since the distance from center to vertex is 6, a = 6.

There's one more relationship you need to know: b^2+c^2=a^2, where a=distance from center to vertex (as before), b= distance between center and graph, measured vertically (not given), and c=distance from center to focus (not given).

Our job is to identify the coordinates of the foci. To do that, we need c^2, and then c.
If a=6 and b=b (unknown), then c^2=a^2-b^2, or c^2=6^2-b^2.

Answer 12

The foci are at (-c,12) and (c,12). We need to find |c|.

\[c ^{2}=6^2-b^2\]
so
\[c \pm \sqrt{(6^2-b^2)}\]
so your foci are
\[(-\sqrt{6^2-b^2},12) and(\sqrt{6^2-b^2},12)\]

Answer 13

I'm sure all this is a lot to swallow. I expect some of it will not be clear for you, and so encourage you to ask questions if you want clarification of any of it.