Im doing the conic section in algebra and cant figure out how to determine the extent of the graph. Which the graph equation is x^2/16-y^2/25=1 can you please help me this is the only thing i don't understand how to figure it out.
you are looking at a hyperbola with its major axis on the x-axis.
a^2 = 16 , a = ± 4
b^2 = 25 , b = ± 5
so the vertices are (4,0) and (-4,0)
foci:
c^2 = 16+25 = 41
c = ± √41
so foci are (√41,0) and (-√41, 0)
The asymptotes are y = (5/4)x and y = (-5/4)x
Sketch these and sketch a rectangle with points
(4,5), (4,-5), (-4,5), and (-4,-5)
the asymptotes should be diagonals of this rectangle.
Sketch the given hyperbola using the asymptotes and the vertices.
http://www.wolframalpha.com/input/?i=plot+x%5E2%2F16-y%5E2%2F25%3D1