Conics - which is which? 9x^2 - 4y^2 = -144

[Tascja]

Can someone tell me if this equation is an ellipse or a hyperbola???

> 9x^2 - 4y^2 = -144

 

[tkhunny]

Hyperbola.

In the absence of an "xy" term, just look for the negative sign.

The -144 is just a decoy. Consider 4y^2 - 9x^2 = 144.

 

[Tascja]

ok thanks... but when i divide everything by the -144 it makes the sign in between become positive so is that still all right? > x^2/16 + y^2/36 = 1

 

[stapel]

The conics check-list:

* Are there two squared terms?
. . .No: It's a parabola.
. . .Yes: Continue:

. . .* Do the squared terms have the same sign?
. . . . .No: It's an hyperbola.
. . . . .Yes: Continue:

. . . . .* Are the squared terms multiplied by the same value?
. . . . . . .No: It's an ellipse.
. . . . . . .Yes: It's a circle.

Eliz.

 

[tkhunny]

* Does it have an 'xy' term? Well, that's a little trickier.

 

[stapel]

* Does it have an 'xy' term? Well, that's a little trickier.

True enough. But it's a rare school (in my experience) that covers "rotation of axes" before calculus, so the check-list is written with the pre-calculus context in mind.

Eliz.

 

[tkhunny]

But it's a rare school (in my experience) that covers "rotation of axes" before calculus, so the check-list is written with the pre-calculus context in mind.

Ah! I see. It is just another case of my unusual history. I just expect pre-calculus stuff to be covered before calculus. No soap-box, today, but I was tempted.

 

[stapel]

I just expect pre-calculus stuff to be covered before calculus.

You make a valid point: It would make a whole lot more sense to cover this topic in a trigonometry-based pre-calculus course, rather than waiting and ambushing students halfway through calculus.

Eliz.