4x^2-25y^2=100

Question

use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equation of the asymptotes.

Answer 1

Ashley,

 

The standard formula of a hyperbola is (x-h)^2/a^2-(y-k)^2/b^2=1 where (h,k) is the center and foci are a distance c from h on the x coordinate. The vertices are a fixed distance a from h and b from y. Then by definition a^2+b^2=c^2. The asymptotes are y=+/-(b/a) (x-h) + k.

 

Converting to standard form we need to divide both sides by 100:

x^2/25-y^2/4=1

 

So the center is clearly the origin (0,0). a=5, b=2 and that makes c=sqrt(29)=5.39. This makes the foci (+/-5.39,0) and the asymptote y=+/-.4x

 

Hope that helps!

Answer 2

I'll get you started:

 

factor 4x²-25y² into (2x-5y)(2x+5y)      difference of two squares

 

set each factor equal to zero will give you the equations of the asymptotes.