How do you graph the ellipse #36x^2 + 9y^2 = 324#?
1 Answer
The most efficient way is to simplify the equation, find crucial points, and plot them on the graph.
Explanation:
For future reference: Formula for equation of vertical hyperbola
We need this equation in a more simplified form since the standard form must be equal to 1:
We can name some crucial values right from our equation. For instance, the center is
Let's graph this! We can set the center at
Vertices:
The covertices are
Covertices:
The foci are on the same line, the major axis, but are
Foci:
We can plot these points on a graph and try our best to draw a smooth line through the vertices and covertices. While the line doesn't pass through the foci, it's still an important part of the ellipse you need to know.
Here's a graph of the ellipse in case you're confused:
graph{x^2/9+y^2/36=1 [-20, 20, -10, 10]}