Sketch the hyperbola with distance between the foci 10 units and the difference of the distances 6 units.

Question

Sketch the hyperbola with distance between the foci 10 units and the difference of the distances 6 units. ​

Quizplus · Accepted Answer

The equation of the hyperbola with distance between the foci $2c=10$ and the difference of the distances $2a=6$ is given by $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $c^2=a^2+b^2$. Solving for $a$ and $b$, we have $a=3$ and $b=4$. Thus, the equation of the hyperbola is $\frac{x^2}{9}-\frac{y^2}{16}=1$, which corresponds to the graph in choice (C).

Sketch the Hyperbola with Distance Between the Foci 10 Units