SOLUTION: I have a "conic invasion" worksheet. I have to tell by the equation the type of figure and the specific info needed to graph the equation. PLEASE HELP ME! im not asking for the ans

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I have a "conic invasion" worksheet. I have to tell by the equation the type of figure and the specific info needed to graph the equation. PLEASE HELP ME! im not asking for the ans      Log On


   

Question 195669: I have a "conic invasion" worksheet. I have to tell by the equation the type of figure and the specific info needed to graph the equation. PLEASE HELP ME! im not asking for the answers or anything (unless youre feeling generous :) just how to get these started im totally lost.
1.y^2+9(x+13)^2=9
2.x^2+y^2=144 for 10>or=y>or=-12
3.x^2+y^2+10x-10y+46=0
4.y+1=0 for 2>or=x>or=-2
5.2x^2-49y+392=0 for y 6.(y^2)/9 + [(x-13)^2]/1=1
7.3x+2y=4 for 2>or=x>or=0
8.2x^2-49y=294 for y 9.15x+7y=175 for 7>or=x>or=-2
10.5x^2-49y=441 for y 11.15x-7y+175=0 for 0>or=x>or=-2
12.3x-2y+4=0 for 0>or=x>or=-2
13.(x-5)^2+(y-5)^2=4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Method # 1

Simply get each equation into the form Ax%5E2%2BBxy%2BCy%5E2%2BDx%2BEy%2BF=0 and use the following properties:



If B%5E2-4AC%3C0, A=C and B=0, then the equation is a circle


If B%5E2-4AC%3C0 and A%3C%3EC, then the equation is an ellipse


If B%5E2-4AC=0, then the equation is a parabola


If B%5E2-4AC%3E0, then the equation is a hyperbola





Method # 2:

Try to get each equation into one of the following forms:


Circle: %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

Ellipse: %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1

Hyperbola: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 (parabolas open in x-direction)

Hyperbola: %28y-k%29%5E2%2Fb%5E2-%28x-h%29%5E2%2Fa%5E2=1 (parabolas open in y-direction)

Parabola (vertex form): y=a%28x-h%29%5E2%2Bk, or

Parabola (vertex form): y=ax%5E2%2Bbx%2Bc (standard form)