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The equation of the ellipse that has a center at (0,0) , a focus at (3 , 0) , and a vertex at (5 , 0 ) , is (x^2)/(A^2)+(y^2)/(B^2)=1

where A =____

B =_______

Guest Jun 13, 2015

#1**+10 **

The equation is given by :

x ^2 / 25 + y ^2 / 16

So ... A = 5 and B = 4

Here's the graph.......https://www.desmos.com/calculator/pfvhokujae

CPhill Jun 13, 2015

#2**+10 **

http://www.mathopenref.com/coordgeneralellipse.html

If the centre is (0,0)

Let the end of the horizontal axis is A(5,0)

The foci is $$S_1(3,0)$$

If you sketch this it is easy to see that the other foci is $$S_2(-3,0)$$

Let the point B(0,b) be the end of the vertical axis.

NOW

$$\\S_1B=BS_2

S_1A+AS_2\;\; must\; \;equal \;\; S_1B+BS_2\\\\

2+8=S_1B+BS_2\\\\

10=5+5\\\\

so\\\\

B(0,4)\\\\

$equation of the ellipse$\\\\

\frac{x^2}{5^2}+\frac{y^2}{4^2}=1\\\\

\frac{x^2}{25}+\frac{y^2}{16}=1$$

Melody Jun 13, 2015