Posted by **Jordan** on Tuesday, April 3, 2007 at 11:20pm.

How do I complete the square:

4x^2+3y^2+8x-6y-5=0

Also, is this a ellipse or a circle?

first of all arrange the terms that appear to 'belong' together

4x^2 + 8x + 3y^2 - 6y = 5

factor out the 4 from the x terms and the 3 from the y terms

4(x^2 + 2x + ??) + 3(y^2 - 2y + ??)=5

take 1/2 the coefficient of the middle term, square it, then add it

4(x^2 + 2x + 1) + 3(y^2 - 2y + 1) = 5 + 4 + 3

notice I added the 1 inside the bracket which was multiplied by 4, so really I added 4, in the same way for the y terms I added 1 to the inside, but that was multiplied by 3, so really I added 3

that is why on the right side you see a 4 and a 3 added.

now express it in the standard form of an ELLIPSE

4(x+1)^2 + 3(y-1)^2 = 12

and finally divide every term by 12 to get

(x+1)^2 /3 + (y-1)^2 /4 = 1

which I hope you recognize as an ellipse and hope you can read off its properties

## Answer this Question

## Related Questions

- Math - how an I tell if this is a circle or an ellipse? also, how am I supposed ...
- Algebra - I need help filling in the blank and answering the question. 1. If you...
- geometry - The area of an ellipse in the form (x*x/a*a)+(y*y)/(b*b)=1 is A=3.14*...
- Math - help me solve this conic: 12x^2+y^2+6x-9=0 not sure what you mean by "...
- Algebra - I am trying to factor polynomials by grouping the first two terms and ...
- Physics - Uniform Circular Motion: Suppose that a particle's position is given ...
- Computing - Write a program that displays the following menu: 1 = Square 2 = ...
- Math - The first three terms of a GP are also the first,nineth and eleventh ...
- Algebra 1: Help Please URGENT! - A circle is inscribed in a square. The number ...
- Algebra 1 - A circle is inscribed in a square. The number of square units in the...