Q:

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

Accepted Solution

A:
Answer: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 Β 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