1. ## Analytic Geometry: Ellipse

Question:
Find the coordinates of the foci, the ends of the major axis and minor axis and the ends of the latus rectum.

Attempt:

$\displaystyle \frac{y^2}{25} + \frac{x^2}{9} = 1$

$\displaystyle a = 5, b = 3, c = \sqrt{a^2-b^2} \rightarrow c=\sqrt{25-9} = 4$

Foci $\displaystyle \rightarrow$ (0,-4) and (0,4)
Ends of Major axis $\displaystyle \rightarrow$ (0,-5) and (0,5)
Ends of Minor axis $\displaystyle \rightarrow$ (-3,0) and (3,0)

Ends of latus rectum:
Left $\displaystyle \rightarrow \left( -4,\frac{9}{5} \right)$ and $\displaystyle \left( -4,-\frac{9}{5} \right)$
Right $\displaystyle \rightarrow \left( 4,\frac{9}{5} \right)$ and $\displaystyle \left( 4,-\frac{9}{5} \right)$

2. Hello, looi76!

Ya done real good!

3. ## Ellipse

Hello looi76
Originally Posted by looi76

Ends of latus rectum:
Left $\displaystyle \rightarrow \left( -4,\frac{9}{5} \right)$ and $\displaystyle \left( -4,-\frac{9}{5} \right)$
Right $\displaystyle \rightarrow \left( 4,\frac{9}{5} \right)$ and $\displaystyle \left( 4,-\frac{9}{5} \right)$
The major axis lies along the y-axis, so I think these coordinates should be the other way around: $\displaystyle \Big(\pm\frac95, \pm 4\Big)$