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