QR: triangle inside eclipse
Started by joonkimdds
In an ellipse the major axis=A minor axis=B foci=C
the eqn for these points is A^2 = B^2 + C^2
if you were using the pythagorean theorem to find the length of the hypotenuse you would use:
B^2 + C^2 = (hypotenuse)^2
so in an ellipse, the major axis is equal to the hypotenuse of the of the triangle formed by the minor axis (B) and a foci (C)
the eqn for these points is A^2 = B^2 + C^2
if you were using the pythagorean theorem to find the length of the hypotenuse you would use:
B^2 + C^2 = (hypotenuse)^2
so in an ellipse, the major axis is equal to the hypotenuse of the of the triangle formed by the minor axis (B) and a foci (C)
Look man. I'm all for helping people in math. But this is a REALLY EASY question. That is a RIGHT TRIANGLE with hypotenuse = a leg. Does that ever happen?
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But as predentgirl said
"so in an ellipse, the major axis is equal to the hypotenuse of the of the triangle formed by the minor axis (B) and a foci (C)"
Although I don't think it makes sense, the rule says it can happen.
The foci are fixed points on the ellipse. They cannot be moved.
I am not sure but that was the whole point of my question.
B^2 + C^2 = A so we know that hyp of triangle is is A
Also at the same time, A is the major axis.
And what predentgirl said is same as what I read from a math book.
"the major axis is equal to the hypotenuse of the of the triangle formed by the minor axis (B) and a foci (C)"
But like streetwolf said, I don't think right triangle can have hyp equal to another side.
This is why I am confused.
Predentgirl said it right. If you make a triangle using the minor axis as one leg, and one of the foci as the third point, the hypotenuse will be the same length as the major axis. And no, you can't move the leg way out to the side because you no longer are using the foci which are intrinsic to each ellipse.
So i guess the first figure I posted is correct, but the 2nd figure is wrong?
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