Hyperbola

[ZyzzBrah]

Fin the equation of the hyperbola with transverse axis on the y-axis, slope of asymptote numerically equal to nine-tenths of the conjugate axis, one vertex at (0,-9)?

asymptote // to y axis
slope of m = a/b = (9/10)* (2b)
b^2 = (10/18)*a
now what

 

[tkhunny]

Maybe c^2 = a^2 + b^2 followed by a = 9? Why did you quit?

 

[ZyzzBrah]

Maybe c^2 = a^2 + b^2 followed by a = 9? Why did you quit?

how did you know that the center is at the origin?

 

[tkhunny]

I didn't. It was an assumption that I failed to state. Good work.

It is a reasonable, simplfying assumption for an initial attempt. It should lead to exploration and perhaps generalization.