Find the values of a and b — the absolute value of the nonzero coordinates of a vertex and a co-vertex.
24
Practice makes perfect
For our ellipse, we are told that the length of the major axis is 30 and the length of the minor axis is 18. We want to find the distance between the foci. Note that this can also be called the focal distance. Before we do this, let's review a few key concepts.
Variable
Relation to the Equation of an Ellipse
a
Absolute value of the nonzero coordinate of the vertices — half the length of the major axis.
b
Absolute value of the nonzero coordinate of the co-vertices — half the length of the minor axis.
c
Absolute value of the nonzero coordinate of the foci — half the length of the focal distance.
If we use the given information to find the values of a and b, we can then use a modified version of the Pythagorean Theorem to find the value of c. Let's start by finding a.
Knowing that a=15 and b=9, we can write an equation to find c.
c=sqrt(a^2-b^2) ⇒ c=sqrt(15^2-9^2)
Let's evaluate the right-hand side of the above equation.
