## Stuck on Finding an Equation for an Ellipse

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.

### Stuck on Finding an Equation for an Ellipse

I follow the exact steps on this problem as demonstrated in my text, and my homework submission website spits this back as wrong every time. Could someone please help me find what I'm missing here?

Find an equation for the ellipse that satisfies the given conditions:

Length of the major axis: 26

The foci are on the x-axis

Ellipse passes through the point $(sqrt3, 6)$

The length of the major axis is $2a=26, a=13$

Foci are in the form $(+ or - c, 0)$ since they're on the x-axis

So far: $(x^2/13^2) + (y^2/b^2) = 1$

Plugging in the (x,y) points I get:

$((sqrt3)^2)/13^2 + (6^2/b^2) = 1$ which simplifies to:

$(3/169) + (36/b^2) = 1$

Subtract (3/169) from 1 and I get: $(36/b^2) = (166/169)$

These can't reduce to whole numbers in both the numerators and denominators--tried it several times.

Therefore I cross-multiply and get $(b^2) = (3042/83)$, which also can't reduce.

$c^2 = a^2-b^2$ for an ellipse, so $(c^2) = 169 - (3042/83)$, which comes out to:

$(c^2) = (10985/83)$

Going back to the equation, I get $(x^2/169) + (y^2/(3042/83)) = 1$

The homework site won't take it, I'm stumped and don't know where I'm messing this up

Thanks in advance for any help!
agenta1013

Posts: 7
Joined: Thu Oct 17, 2013 2:20 pm

### Re: Stuck on Finding an Equation for an Ellipse

agenta1013 wrote:I follow the exact steps on this problem as demonstrated in my text, and my homework submission website spits this back as wrong every time.

the HW had a problem just the same as in the lesson? i think somebody messed up somewhere! maybe theres a typo???

agenta1013 wrote:Find an equation for the ellipse that satisfies the given conditions:
Length of the major axis: 26
The foci are on the x-axis
Ellipse passes through the point $(sqrt3, 6)$

i agree w/ a=13 but they dont say that its centered at (0,0) but i dont see any way to do this w/o assuming so, right? so (h,k)=(0,0). & so i agree w/ what the foci look like. & i agree w/ 3/169 + 36/b^2 = 1 & c^2 = 10985/83

agenta1013 wrote:I get $(x^2/169) + (y^2/(3042/83)) = 1$

The homework site won't take it

maybe they want it like x^2/169 + 83y^3/3042 = 1 so the fraction is flipped? if it doesnt take that then go ask your teacher or else tech support
buddy

Posts: 125
Joined: Sun Feb 22, 2009 10:05 pm

### Re: Stuck on Finding an Equation for an Ellipse

buddy wrote:
agenta1013 wrote:I follow the exact steps on this problem as demonstrated in my text, and my homework submission website spits this back as wrong every time.

the HW had a problem just the same as in the lesson? i think somebody messed up somewhere! maybe theres a typo???

Guess I could've explained that better--the text has a few practice problems just like this with smaller, simpler values. I've gotten those correct, just not this online HW one.

agenta1013 wrote:Find an equation for the ellipse that satisfies the given conditions:
Length of the major axis: 26
The foci are on the x-axis
Ellipse passes through the point $(sqrt3, 6)$

i agree w/ a=13 but they dont say that its centered at (0,0) but i dont see any way to do this w/o assuming so, right? so (h,k)=(0,0). & so i agree w/ what the foci look like. & i agree w/ 3/169 + 36/b^2 = 1 & c^2 = 10985/83

agenta1013 wrote:I get $(x^2/169) + (y^2/(3042/83)) = 1$

The homework site won't take it

maybe they want it like x^2/169 + 83y^3/3042 = 1 so the fraction is flipped? if it doesnt take that then go ask your teacher or else tech support

Thanks; I'll give that a try
agenta1013

Posts: 7
Joined: Thu Oct 17, 2013 2:20 pm