Graph the conic section.
25x2 – 16y2 = 400
This is the equation of a hyperbola.
To graph it, we can rewrite the equation as:
x^2/16 - y^2/25 = 1
Now, we can see that this is a hyperbola with the center at the origin, with vertices along the x-axis and asymptotes passing through the center.
The standard form for the equation of a hyperbola with vertices along the x-axis and center at the origin is:
(x^2/a^2) - (y^2/b^2) = 1
Here, a^2 = 16 and b^2 = 25, so a = 4 and b = 5.
This means that the vertices are at (4,0) and (-4,0), and the asymptotes are given by y = (5/4)x and y = -(5/4)x.
We can now plot the vertices, asymptotes, and the curve to graph the hyperbola.
The red curve represents the hyperbola, and the blue lines are the asymptotes.
It should look like this:
graph: x^2/16 - y^2/25 = 1