Question

I need serious help!
what are the foci of the hyperbola with equation 9y^2-16x^2=144

Answer 1

no one likes these conic section problems, but they are not that hard
first of all you need to have an idea of what it looks likek
do you know what the picture is?

Answer 2

No

Answer 3

ok you need that first
lets start by dividing everything by \(144\) to make it look like
\[\frac{y^2}{a2}-\frac{x^2}{b^2}=1\]

Answer 4

you should get \[\frac{x^2}{16}-\frac{y^2}{9}=1\]and now believe it or not we are almost done

Answer 5

but first you need to know what it looks like

Answer 6

any guesses?

Answer 7

Is it \[(\pm5,0)\]

Answer 8

No, those a re switched, so it's \[(0,\pm5)\]

Answer 9

@satellite73

Answer 10

the picture is the one on the right, since the \(y^2\)term comes first

Answer 11

so yeah, the foci are \((0,5)\) and \((0,-5)\)