Identify the conic section, any lines of symmetry, and the domain and range.

x = 2y^2 + 5 , please help!!

Question

Identify the conic section, any lines of symmetry, and the domain and range.

x = 2y^2 + 5 , please help!!

owlcoffee · Answer

A conic section have a general equation of $$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$$
And this can be accomodated to fit any type of equation you have learned so far, this being: (1) A circle, (2) a parabola, (3) an elipse, (4) a hyperbola, (5) a product of lines.
This is mostly evident through the discriminant $\Delta=B^2-4AC$:
(a) if $\Delta>0$ then the conic section has hiperbolic genre
(b) if $\Delta=0$ then the conic section has Parabolic genre
(c) if $\Delta < 0$ then the conic section has eliptic genre.

This is saved for when the conic section is complete and hard to represent, but in any case, your equation:
$$x=2y^2+5$$
Respects the form $x=ay^2+by+c$ and that equation represented what geometric body?

pokiedokie · Answer

a hyperbola, and the domain would be 5, and i'm really not sure about anything else like the range? would it be 2?

pokiedokie · Answer

@Owlcoffee

pokiedokie · Answer

nvm i've figured some of it out, it's a parabola

owlcoffee · Answer

Good, now, what are the components of a parabola?

pokiedokie · Answer

the x and y intercepts and axis of symmetry?