Question

One of the biggest challenges in working with conic sections is to look at an equation in standard form and determine which section it describes. Can someone please explain to me how you determine which conic section a particular equation describes??

Answer 1

@ranga

Answer 2

You can tell by looking at the equation forms
For a hyperbola:
\[\huge \frac{ (x-h)^2 }{ a^2 } - \frac{(y-k)^2 }{ b^2 }\]
For a circle:
\[\huge (x-h)^2 + (y-k)^2 = r^2\]
For an ellipse:
\[\huge \frac{ (x-h)^2 }{ a^2 } + \frac{ (y-k)^2 }{ b^2 } = 1\]

Answer 3

forgot to add for the hyperbola its also equal to 1*

Answer 4

thank you! :)

Answer 5

I will just add parabola to the above:

(x – h)^2 = 4p(y – k) -------- vertical axis parabola
(y – k)^2 = 4p(x – h) -------- horizontal axis parabola.