Is this a trick question from my exam? (1 Viewer)

[hayabusaboston]

I got a question today in an ext 2 test and it literally said,
"The general equation of a hyperbola is x^2/a^2 - y^2/b^2
If this hyperbola passes through the point P(15,16), what is the equation of the hyperbola?"

Am I missing something or is this a stupidly simple question??

 

[seanieg89]

I got a question today in an ext 2 test and it literally said,
"The general equation of a hyperbola is x^2/a^2 - y^2/b^2
If this hyperbola passes through the point P(15,16), what is the equation of the hyperbola?"

Am I missing something or is this a stupidly simple question??

Its not stupidly simple, its just stupid. There are infinitely many such hyperbolas that pass through the point (15,16).

 

[lochnessmonsta]

I did my test today too yay! Hoping for ~95%

 

[jyu]

I got a question today in an ext 2 test and it literally said,
"The general equation of a hyperbola is x^2/a^2 - y^2/b^2
If this hyperbola passes through the point P(15,16), what is the equation of the hyperbola?"

Am I missing something or is this a stupidly simple question??

x^2/a^2 - y^2/b^2 is not an equation

 

[Viscass]

there must have been more information

 

[Nws m8]

Its not stupidly simple, its just stupid. There are infinitely many such hyperbolas that pass through the point (15,16).

+1

 

[hayabusaboston]

omg its pretty obvious It is x^2/a^2 - y^2/b^2=1 isnt it? I said "hyperbola" lol

that was literally the only info given. I was totally "wtf" on it haha.

 

[anomalousdecay]

[QUOTE/] Its not stupidly simple, its just stupid. There are infinitely many such hyperbolas that pass through the point (15,16). [/QUOTE]

Then don't you have to find the locus in terms of a and b?

 

[seanieg89]

The locus of what?

The best one could do is eliminate either a or b and get a one-parameter family of hyperbolas passing through the given point.

 

[anomalousdecay]

I'm assuming your right, but when you say one-parameter families, isn't that the same as the locus of P?

I'm probably wrong, but I'm confused.

 

[seanieg89]

The locus of P? P is the fixed point (15,16), it does not vary.

Remember, a locus is a set of points, not a set of cuves.

 

[anomalousdecay]

The locus of P? P is the fixed point (15,16), it does not vary.

Right, that makes sense now. So this is a written question where you just say that you get a family of conics with the one parameter. Wow, I have never seen that before.

 

[seanieg89]

Nah, they wouldn't want that. The question is just wrong, missing a piece of information or something. (They clearly asked for the equation of the hyperbola.)