SOLUTION: How do you write this equation of ellipse in simple form? 3x^2 + 4y^2 + 8y=8 * I tried dividing everything by eigth leaving me with: 3x^2/8 +y^2/2 + y=1

Question 118267: How do you write this equation of ellipse in simple form?
3x^2 + 4y^2 + 8y=8

* I tried dividing everything by eigth leaving me with:
3x^2/8 +y^2/2 + y=1
But when i checked to see if i had the right answer i got it wrong this is the correct answer:
x^2/4 + (y+1)^2/3=1

I don't understand why i got the problem wrong.

Found 3 solutions by jim_thompson5910, stanbon, Earlsdon:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Factor out 4 from to get

Take half of the "y" coefficient 2 to get 1. Now square 1 to get 1. Add this and it's opposite -1 inside the parenthesis. Notice how 1-1=0 so it does not change the equation.

Factor to get

Distribute

Add 4 to both sides

Combine like terms

Now Divide both sides by 12 to get the right side equal to one. With any ellipse, we always want the right side equal to one.

Break up the fraction on the left side.

Reduce

So the ellipse in standard form is . Remember, we are trying to go from something like to . Looking at your answer, notice how you have an extra "y" which does not fit the standard equation of an ellipse. This is why you must complete the square to get the equation to fit the form. Does that make sense?
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
3x^2 + 4y^2 + 8y=8
3x^2 + 4(y^2+2y+1) = 8+4
3x^2 + 4(y+1)^2 = 12
3x^2/12 + 4(y+1)^2/12 = 1
x^2/4 + (y+1)^2/3 =1
========================
Cheers,
Stan H.

Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
The standard form for the equation of an ellipse with center at (h, k) and major axis parallel to the x-axis is: (a is the semi-major axis and b is the semiminor axis)
or, if the major axis is parallel to the y-axis:

Starting with the given equation:
Group the terms as shown:
Now factor a 4 from the y-group.
Now complete the square in the y-terms inside the parentheses by adding the square of half the y-coefficient or (), remembering that you are really adding 4 because of the 4 in front of the parentheses.
Now simplify this by factoring the trinomial in the y-terms.
Now divide through by 12 to get the right side equal to 1.
Simplify this.

RELATED QUESTIONS
How do I write the equation of the ellipse {{{9x^2 + 4y^2 - 36x + 24y + 36 = 0}}} in... (answered by drk)
I have to find the Domain of g(x)= 3-2√(5-x). i've gone on to mathway.com where it... (answered by josmiceli,josgarithmetic)
i need to complete the square to write the equation so that the right side is in the... (answered by venugopalramana)
I am trying to simplify the equation for an ellipse so that it is in the standard form of (answered by lwsshak3)
Write this ratio in simplest form: 1/10 / 1/4 First I must flip the second problem: (answered by ptaylor)
I can’t find the x- and y-intercepts of this equation: {{{4y + 5x = 2y - 3x + 16}}}. I... (answered by Alan3354,MathTherapy)
Please Can you help me !!!!! Write each equation in standard form. State whether the... (answered by ewatrrr)
Hi, please help me solve this ellipse equation by putting it in standard form. {{{4x^2 + (answered by math problem solving)
How do I find the starndard form of an ellipse with the equation... (answered by stanbon)