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Question 607718: State whether the equation is a parobola, circle, or and elipse. Write the equation in the appropriate standard form and then give all the associated "pieces."
5x^2+2y^2+30x-16y=-67
Thanks for any help you can give us!
michelle@modesto.net
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 5x^2+2y^2+30x-16y=-67
5x^2+30x+2y^2-16y=-67
(5x^2+30x)+(2y^2-16y)=-67
5(x^2+6x)+2(y^2-8y)=-67
5(x^2+6x+9-9)+2(y^2-8y+16-16)=-67
5((x^2+6x+9)-9)+2((y^2-8y+16)-16)=-67
5((x+3)^2-9)+2((y-4)^2-16)=-67
5(x+3)^2-5(9)+2(y-4)^2-2(16)=-67
5(x+3)^2-45+2(y-4)^2-32=-67
5(x+3)^2+2(y-4)^2-77=-67
5(x+3)^2+2(y-4)^2=-67+77
5(x+3)^2+2(y-4)^2=10
(5(x+3)^2)/10+(2(y-4)^2)/10=10/10
( (x+3)^2 )/2+( (y-4)^2 )/5 = 1
So this is an ellipse that is centered at (-3,4).
It has a major axis that has a length of 2*sqrt(5) units and minor axis that has a length of 2*sqrt(2) units.
Note: the general form of an ellipse is ( (x-h)^2 )/(a^2)+( (y-k)^2 )/(b^2)=1
The center of this general ellipse is (h,k).
The length of the major axis of this general ellipse is 2a (where a > b)
The length of the minor axis of this general ellipse is 2b (where a > b)
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