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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

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 #3
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Melody  Jun 13, 2015
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 #1
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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
avatar+90988 
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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
 #3
avatar+90988 
+10
Best Answer

Melody  Jun 13, 2015

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