sarah1017
What is the standard form of the equation of an ellipse with foci at (+3,0) and covertices at (0,+5)?
Please show all steps!



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ganeshie8
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dw:1393563390845:dw

ganeshie8
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dw:1393563452971:dw

ganeshie8
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dw:1393563500603:dw

ganeshie8
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b = 5
a = ?

ganeshie8
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if u can find a, u can write the equation of ellipse :
\(\large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

ganeshie8
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any idea how to find "a" ? :)

sarah1017
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How do I find a? Is there a formula I have to follow?

ganeshie8
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u just need to knw how to find an unknown side in a right triangle

sleung
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Use the pythagorean theorem.

ganeshie8
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dw:1393563687257:dw

ganeshie8
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a^2 = b^2 + c^2
a^2 = 5^2 + 3^2

ganeshie8
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simplify

sarah1017
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a^2=34

ganeshie8
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yes, you want "a" right ?

sarah1017
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Yes. So do I divide 34 by 2?

ganeshie8
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noo, you need to take "square ROOT" both sides

sleung
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So \[a=\sqrt{34}\]

sarah1017
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5.83

ganeshie8
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actually im wrong,
a^2 is enough as u put it earlier,,,, i see we dont need to find a .

ganeshie8
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directly plugin a^2 value in the equation

ganeshie8
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\(\large \frac{x^2}{34} + \frac{y^2}{25} = 1\)

ganeshie8
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^^final equation of ellipse

sarah1017
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Whoaaa that confused me. So that's the final equation, is the work we did before still correct? Well except the finding a parts?

ganeshie8
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everything is correct,
you could even find "a", and plugin the "a" value back into the equaiton

ganeshie8
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but thats just extra unnecessary work

ganeshie8
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when u knw that u will be needing oly "a^2", why to find "a" ?

ganeshie8
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it wont be a mistake to find "a", its just pain to take square root of 34 lol.. .hope u get me :)

sarah1017
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I wasn't too sure how to do this at first so I just went with ya lol. I get it though. Thanks for your help :)

ganeshie8
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np :) u wlc :))

sarah1017
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:)