Question

Write the equation of a hyperbola with vertices at (1,1) and (9, 1) and foci at (0, 1) and (10, 1).

Answer 1

Standard form of equation for a hyperbola with horizontal transverse axis:

(x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center

For given hyperbola:

x-coordinate of center=(9+1)/2=5 (use midpoint formula)

y-coordinate of center=1

center: (5,1)

length of horizontal transverse axis=8 (from 1 to 9)=2a

a=4

a^2=16

..

Foci

2c=9 ( from 1 to 10)

c=4.5

..

c^2=a^2+b^2

b^2=c^2-a^2=20.25-16=4.25

..

Equation of hyperbola:

(x-5)^2/16-(y-1)^2/4.25=1