Question

Identify the type of conic section that has the equation 9x2+ 16y2 = 144 and identify its domain and range.

ellipse
Domain: {–3 ≤ x ≤ 3}
Range: {–4 ≤ y ≤ 4}


ellipse
Domain: {–4 ≤ x ≤ 4}
Range: {–3 ≤ y ≤ 3}


hyperbola
Domain: all real numbers
Range: {y ≤ –4 or y ≥ 4}


hyperbola
Domain: {x ≤ –4 or x ≥ 4}
Range: all real numbers

Answer 1

What do you think it is? Any ideas?

Answer 2

an ellipse

Answer 3

yes. That's it.

Answer 4

Now divide both sides by 144 to get it into the right form so we can identify "a" and "b" and figure out the domain and range.

Answer 5

so 9x2/144 +16y2/144

Answer 6

Now cancel the 9 and the 16 into the 144

Answer 7

\[\frac{ 9x2 }{ 144}+\frac{ 16y2 }{ 144}=1\]