given the ellipse 3x^2 5y^2-12x-50y 62=0 find a,b,c,d

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Aug 27th, 2015

Hi there! Thank you for the opportunity to help you with your question!

We have to complete the squares for both x and y. for x:

3(x-2)^2 -12

and for y:


Putting it all together:

3(x-2)^2 -12+5(y-5)^2-125 +62 = 0


3(x-2)^2+5(y-5)^2 = 75

dividing both sides by 75:

(x-2)^2/25 + (y-5)^2/15 = 1

The center is (2,5) as shown by the shifts in the x, y arguments in parentheses above

The length of the major axis is sqrt(25) = 5

The length of the minor axis is sqrt(13)

The distance from the focii to the center is sqrt(10)

So the final answer would be:

(2,5), 5, sqrt(13), sqrt(10)

Please let me know if you need any clarification. Always glad to help!
Aug 27th, 2015

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