Precalculus : Find the Foci of a Hyperbola

Example Questions

2 Next →

Example Question #15 : Hyperbolas

Find the foci of the hyperbola with the following equation:      Explanation:

Recall that the standard formula of a hyperbola can come in two forms: and , where the centers of both hyperbolas are .

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following: For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

For the given hypebola in the question, the transverse axis is vertical and its center is located at .

Next, find . The foci are then located at and .

Example Question #16 : Hyperbolas

Find the foci for the hyperbola with the following equation:      Explanation:

Recall that the standard formula of a hyperbola can come in two forms: and , where the centers of both hyperbolas are .

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following: For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

For the given hypebola in the question, the transverse axis is vertical and its center is located at .

Next, find . The foci are then located at and .

Example Question #121 : Conic Sections

Which point is one of the foci of the hyperbola ?      Explanation:

To find the foci of a hyperbola, first determine a and b, and then use the relationship In this case, the major axis is horizontal since x comes first, so and .

Solve for c: add 9 to both sides take the square root Since the center is and the major axis is the horizontal one, our foci are . The only choice that works is .

Example Question #11 : Hyperbolas

Determine the length of the foci for the following hyperbola equation:      Explanation: To solve, simply use the follow equation where c is the length of the foci.

In this particular case,  Thus,  Example Question #21 : Hyperbolas

Find the foci of the hyperbola with the following equation:  and  and  and  and  and  and Explanation:

The standard form of the equation for a hyperbola is given by The foci are located at (h+c, k) and (h-c, k), where c is found by using the formula Since our equation is already in standard form, you can see that  Plugging into the formula So the foci are found at AND 2 Next →

All Precalculus Resources 