Question

1. What are foci? 2. What is the first step to take to write the equation of a hyperbola? 3. How do you represent parts of a hyperbola algebraically?

Answer 1

Answer:  see below

Step-by-step explanation:

1) Foci is plural for Focus.  Since a hyperbola has two focus points, they are referred to as foci.  The foci is where the sum of the distances from any point on the curve to the foci is constant.

2) When determining the equation of a hyperbola you need the following:

    a)  does the hyperbola open up or to the right?

    b)  what is the center (h, k) of the hyperbola?

    c)  What is the slope of the asymptotes of the hyperbola?

3) The equation of a hyperbola is:

$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1$

• (h, k) is the center of the hyperbola
• ± b/a is the slope of the line of the asymptotes
• The equation starts with the "x" if it opens to the right and "y" if it opens up