anonymous
  • anonymous
The line x=25/4 is directrix of an ellipse and its associated focus is the point (4,0), find the equation of the ellipse.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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tkhunny
  • tkhunny
The vertex is half way from the focus to the directrix.
anonymous
  • anonymous
Yes. Then i know that one vertex is (41/8,0) How does that help me?
tkhunny
  • tkhunny
(y-k)^2 = 4p(x-h) Ringing any bells? You will be required on examination to be acquainted with this form.

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anonymous
  • anonymous
ok, but that's the parabola equation. We're talking about ellipse.
tkhunny
  • tkhunny
Right. Just saw that. Sorry. You will not be required to know about a parabola a ellipse question.
tkhunny
  • tkhunny
Directrix, x = 25/4 is "outside" the focus (4,0), so we are to construe via symmetry that the other focus is at (-4,0)? That's not entirely clear to me. I'm thinking we need one more clue. Center at the origin? Eccentricity? Something.
jdoe0001
  • jdoe0001
based on http://mathworld.wolfram.com/Ellipse.html the directrix will be at \(\bf \cfrac{a^2}{c} \implies \cfrac{25}{4} \implies\cfrac{a=5}{c=4}\) then we also know that "c" is the distance from the center to the focus and that \(\bf c= \sqrt{a^2-b^2}\) we know "c" and we know "a" c = 4 a = 5 so what's "b"? well \(\bf \cfrac{a^2}{c} \implies \cfrac{25}{4} \implies\cfrac{a=5}{c=4}\\ c = \sqrt{a^2-b^2} \implies b^2 = a^2-c^2 \implies b = \sqrt{a^2-c^2}\)
anonymous
  • anonymous
Well, that's true if the center of the ellipse is at the origin. And the problem never say that. So i have to assume that as a condition in order to solve the problem?
jdoe0001
  • jdoe0001
well, ... to be honest, we know one focal point, but we dunno where the center might be it could be the origin, or the at (4,4) or (0,-4)
jdoe0001
  • jdoe0001
(4, -4) rather
jdoe0001
  • jdoe0001
but I'd assume any of those valid points for the center will be a valid equation for the requested ellipse
jdoe0001
  • jdoe0001
the picture at wolfram uses the 0,0 origin, yes, but the equation for the directrix is based on the "a" and "c" component, which aren't exclusive to the origin, they're just a scalar value
tkhunny
  • tkhunny
It is easy to assume the origin. If I wanted to impress the teacher, I might assume the eccentricity. It may appear as though one were paying attention! e = 0.8, for example.

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