Graph the hyperbola y 2 $-$ 16 x 2 = 9.

Question

Quizplus · Accepted Answer

First, we need to rewrite the equation in standard form, which is:
 
    (y^2/9) - (x^2/16) = 1
 
We can see that the transverse axis is the y-axis since y^2 is positive and x^2 is negative. The center is (0,0) and the distance from the center to the vertices is 3 units. Hence, the vertices are at (0, ±3).
 
The distance from the center to the foci is given by c = sqrt(a^2 + b^2), where a=3 and b=4. Solving for c gives us c=5. Therefore, the foci are at (0, ±5).
 
The asymptotes can be found using the formula y = ±(b/a)x. Substituting a=3 and b=4, we get the equations y = ±(4/3)x.
 
The graph of the hyperbola should look like this:
 
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Graph the Hyperbola Y 2 −-− 16 X 2 = 9

Graph the Hyperbola Y 2 $-$ 16 X 2 = 9