Can someone please help me with this,

I am suppose to state which type of conic section is represented by each equation step by step if its possible

1. x^2-6x+y=8

2. 3x^2+5y^2+6x-10y=16

3. 2x^2+8x=2y^2-y+10

4. 3x^2+x-y^2+y=12

5. x^2+4y^2=8

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- Nov 12th 2007, 01:39 AMxterminal01[SOLVED] Conic section what each equation represents
Can someone please help me with this,

I am suppose to state which type of conic section is represented by each equation step by step if its possible

1. x^2-6x+y=8

2. 3x^2+5y^2+6x-10y=16

3. 2x^2+8x=2y^2-y+10

4. 3x^2+x-y^2+y=12

5. x^2+4y^2=8 - Nov 12th 2007, 02:10 AMearboth
Hello,

rearrange your equations until you can determine the type of conic. All of them have their axes parallel to the coordinate axes so completing the square will do:

to #1:

That's a parabola opening down.

to #2:

. Now divide by 24 and you'll get:

That's the equation of an ellipse.

The ##3 to 5 should be done similary.(H, H, E) - Nov 12th 2007, 02:15 AMxterminal01
Thanks alot for the help can you please state the step by step for number 3,4,5

- Nov 12th 2007, 02:30 AMearboth
Hi,

I was quite sure that you could do the last problems using the way I demonstrated to you, but .... I'll start the problems and I'll leave the final brush up to you:

to #3:

. Simplify and you should come out with a hyperbola

to #4:

Simplify. It's a hyperbola too.

to #5:

Divide by 8. Then you get the equation of an ellipse. - Nov 13th 2007, 08:03 PMxterminal01
Okey so i tried to finish number 3 and this is what i came up with please check if its right

3 i got stuck with this...

4 i dont know how to finish :confused:

5 should be - Nov 13th 2007, 09:40 PMSoroban
Hello, xterminal01!

Quote:

State which type of conic section is represented by each equation.

First, get all the variables on one side of the equation.

. . (As we did in #3.)

If it has either or ,*but not both*, it is a. .(#1)*parabola*

If and have the same coefficient, it is a. .(None listed)*circle*

If and have the same sign, it is an. .(#2 and 5)*ellipse*

If and have opposite signs, it is a. .(#3 and 4)*hyperbola*

- Nov 13th 2007, 09:48 PMearboth
- Nov 13th 2007, 09:54 PMxterminal01
Yea but i cant solve the equation to the end ...

- Nov 14th 2007, 05:45 AMtopsquark