Question

Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at
y = ±5/6 x.

Answer 1

you'll want to use this again http://www.jfkcougars.org/ourpages/auto/2013/2/5/43231143/Conics-Formula-Sheet.pdf

since the vertices are (0, 10) and (0, -10) its a vertical hyperbola. Center is (0, 0) since that's halfway between the vertices.

Answer 2

(y/b)^2-(x/a)^2 = 1
(y/10)^2-(x/a)^2= 1
lim(f(x)/x)=m
x-infinity
(y/10)^2- (x/a)^2= 1
y = square root of (100 + 100(x/a)^2)
lim (suare root(100 + 100(x/a)^2)/x ) =10/a
x-infinity
10/a =5/6
a =12
(y/10)^2- (x/12)^2= 1

@agent0smith

Answer 3

That looks right to me