Exercise 48 Page 649

The equation of a vertical hyperbola is $\frac{( y - k ) ^{2}}{a ^{2}} - \frac{( x - h ) ^{2}}{b ^{2}} = 1 .$ The vertices are $(h, k \pm a) .$ How can you find the foci and the asymptotes?

Vertical Hyperbola with Center $(h, k)$
Equation	$\frac{( y - k ) ^{2}}{a ^{2}} - \frac{( x - h ) ^{2}}{b ^{2}} = 1$
Transverse axis	Vertical
Vertices	$(h, k \pm a)$
Foci	$(h, k \pm c),$ where $c^{2} = a^{2} + b^{2}$
Asymptotes	$y - k = \pm \frac{a}{b} (x - h)$

Equation	$\frac{( y - ( - 1 ) ) ^{2}}{4 ^{2}} - \frac{( x - 4 ) ^{2}}{3 ^{2}} = 1$
Transverse axis	Vertical
Vertices	$(4, 3)$ and $(4, - 5)$
Foci	$(4, 4)$ and $(4, - 6)$
Asymptotes	$y = \pm \frac{4}{3} (x - 4) - 1$

Exercise 48 Page 649

Hints

Check the answer

Practice exercises

Asses your skill

Vertices, Foci, and Asymptotes

Graph