Determine whether the transverse axis and foci of the hyperbola are on the -axis or the -axis.

The transverse axis and foci of the hyperbola are on the -axis.
The transverse axis and foci of the hyperbola are on the -axis.

Ask by Hall Simmons. in the United States

Mar 25,2025

Question

Determine whether the transverse axis and foci of the hyperbola are on the -axis or the -axis.

The transverse axis and foci of the hyperbola are on the -axis.
The transverse axis and foci of the hyperbola are on the -axis.

Ask by Hall Simmons. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

We start with the given equation:
$$
-x^2 + \frac{y^2}{20} = 1.
$$
Our goal is to rewrite the equation in standard form for a hyperbola.

1. Rearranging the terms, we write:
$$
\frac{y^2}{20} - x^2 = 1.
$$
2. Compare this with the standard form of a hyperbola:
   - For a hyperbola with a vertical transverse axis:
     $$
     \frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2}=1,
     $$
     where the center is at $$(h,k)$$.
   - In our equation, there are no shifts (i.e., $$h = 0$$ and $$k = 0$$), and it matches the form with $$a^2 = 20$$ and $$b^2 = 1$$.

3. Since the $$y$$-term is positive and comes first, the transverse axis is vertical. The foci lie along the transverse axis (which is the $$y$$-axis).

Thus, the transverse axis and foci of the hyperbola are on the $$ y $$-axis.
The transverse axis and foci of the hyperbola are on the $$ y $$-axis.

Determine whether the transverse axis and foci of the hyperbola are on the -axis or the -axis.

The transverse axis and foci of the hyperbola are on the -axis.
The transverse axis and foci of the hyperbola are on the -axis.

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Determine whether the transverse axis and foci of the hyperbola are on the -axis or the -axis. The transverse axis and foci of the hyperbola are on the -axis. The transverse axis and foci of the hyperbola are on the -axis.

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Latest Pre Calculus Questions

Determine whether the transverse axis and foci of the hyperbola are on the -axis or the -axis.

The transverse axis and foci of the hyperbola are on the -axis.
The transverse axis and foci of the hyperbola are on the -axis.