Question

Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (0, 11), and a co-vertex at (4, 0). HELP ASAP

Answer 1

Answer:

Step-by-step explanation:

If you plot those points on a coordinate plane, you'll see that the distance from the origin up the y-axis to the point is greater than is the distance from the origin down the x-axis to the other point. That means 3 things to us: 1. the greater distance is a and the shorter is b; 2. the point (0, 11) is the vertex while the point (4, 0) is the co-vertex; and 3. this is a vertically stretched ellipse. A vertically stretched ellipse has an equation

$\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1$ where h and k are the coordinates of the center, a is the greater distance (between the center and the vertex), and b is the smaller distance (between the center and the co-vertex).  Here's what we have then thus far:

h = 0

k = 0

a = 11

b = 4

Filling in our equation then looks like this:

$\frac{(x-0)^2}{4^2} +\frac{(y-0)^2}{11^2} =1$ and simplifying:

$\frac{x^2}{16} +\frac{y^2}{121} =1$. It appears that the last answer is the one you want, although when I teach this to my precalc students, I do not encourage them to move the x and y terms around as that answer appears to have done. But addition is also commutative so I'm sure it's acceptable (I just think it looks strange that way).