Module 7: Conics
Lesson 2 Notes
Ellipse
Video 3 Transcript
Hey everyone this is a video for module 7 lesson 2 ellipse notes video 3.
In this video we are going to be finding the equation of the ellipse with a foci at (0,8)
and (0,-8) and a major axis with a length of 24. So I am just going to go ahead and
draw a sketch of what my example is telling me here. So I know I have a foci at (0,8)
and at (0,-8). And I know I have a major axis with a length of 24. So since my foci is
on the y-axis I know my major axis has to be on the y-axis as well. So, if it has a
length of 24 then that means that means there is a length of 12 here and 12 here. So
I am going to have (0,12) here and (0,-12) here. So if you remember from the notes
and the last video, the foci value actually comes from the “c” value. Since our major
axis is running this way and that is the y-axis, we know that in my regular formula
lets just say it looks like this. I know that it is centered around (0,0) because my foci
is here and its even, symmetrical. So I know that my major axis, my “b” squared had
to be larger than my “a” squared because my major axis is here. So I know that my
“b” value had to be 12 so the “b” squared would have to be 144. What I don’t know is
my “a” squared.
But since my “b” squared value would be larger than my “a” squared, that’s how my
major axis was determined, then I know that to find the “c” value. I would have used
“b” squared minus “a” squared equals “c” squared. Ok, so my “b” squared would be
144. I don’t know my “a” squared, that’s what I am solving for. Now “c” squared
actually comes from the foci, since my foci is (0,8) I know that 8 is the length of my
“c”. So I know that “c” is 8, that is 8 squared. 144 minus “a” squared is 64.
So I want to subtract 144 from both sides. So 64 minus 144 and that would be
negative “a” squared equals -80. “a” squared would equal 80. So I am actually
looking for the “a” squared value. So I can stop right there, I don’t need to solve for
“a” all the way.
𝑥2
𝑦2
So my formula for this would be 80 + 14 = 1. And that would be the formula.