graph-the-hyperbola-defined-by-4x2-25y2-100-using-its-vertices-and-asymptotes-th

Question

Graph the hyperbola defined by 4x² - 25y² = 100 using its vertices and asymptotes. Then, determine the equations of the asymptotes and the foci.

Accepted Answer

Foci: (-√29, 0) and (√29, 0); Asymptotes: y = ± (2/5)x

Graph of a hyperbola with vertices at (-5,0) and (5,0), showing asymptotes.

Answer

Foci: (0, -√29) and (0, √29); Asymptotes: y = ± (5/2)x

Graph of a hyperbola with vertices at (0,-5) and (0,5), showing asymptotes.

Answer

Foci: (-29, 0) and (29, 0); Asymptotes: y = ± (4/25)x

Graph of a hyperbola with vertices at (-25,0) and (25,0), showing asymptotes.

Answer

Foci: (0, -29) and (0, 29); Asymptotes: y = ± (25/4)x

Graph of a hyperbola with vertices at (0,-25) and (0,25), showing asymptotes.

Graph the hyperbola defined by 4x2 - 25y2 = 100 using its vertices and asymptotes. Then, determine the equations of the asymptotes and the foci.