SOLUTION: Graph the hyperbola. Label the x or y intercepts for the "branches". Also, show the asymptotes and the foci. Please show the graph. 5x^2-20y^2=100

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Graph the hyperbola. Label the x or y intercepts for the "branches". Also, show the asymptotes and the foci. Please show the graph. 5x^2-20y^2=100      Log On


   

Question 438710: Graph the hyperbola. Label the x or y intercepts for the "branches". Also, show the asymptotes and the foci. Please show the graph.
5x^2-20y^2=100
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, Note: 

Standard Form of an Equation of an Hyperbola opening right and left is  

            %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 

where Pt(h,k) is a center  with vertices 'a' units right and left of center.

  5x^2-20y^2=100

%28x%29%5E2%2F20+-%28y%2B2%29%5E2%2F5+=1  C(0,0) with vertices V(0,-2sqrt%285%29) and V(0,2sqrt%285%29)

Domain: {x ≥ 2sqrt%285%29), x ≤ -2sqrt%285%29) }  

Range:

Foci(c=sqrt%2825%29=5): F(-5,0) and F(5,0)

Asymptotes:   y = .5x and y = -.5x