Identify the type of conic section that has the equation 9x^2+ 16y^2 = 144 and identify its domain and range.

Question

anonymous · Answer

A parabola is in the form$$
4py=x^2
$$
An ellipse is in the form$$
\left(\frac{x}{a}\right)^2+\left(\frac{y}{b}\right)^2=1
$$

A hyperbola is in the form$$
\left(\frac{x}{a}\right)^2-\left(\frac{y}{b}\right)^2=1
$$

anonymous · Answer

oh.. so i would solve for those values and plug them in?

anonymous · Answer

Nope.  Just think of which one your equation looks most similar to

anonymous · Answer

oh.. well i would say the second one. is that right?

anonymous · Answer

Yeah, so what is it called?

anonymous · Answer

a hyperbola?

anonymous · Answer

... no it says ellipse.

anonymous · Answer

the second one does?

anonymous · Answer

"An ellipse is in the form"
This is me saying "this second equation here is for an ellipse"

anonymous · Answer

oh.. got it. sorry, I found this really confusing. So then the domain would be all real numbers right?

anonymous · Answer

No, the domain is between $[-a, a]$ and the range is between $[-b,b]$

anonymous · Answer

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