# Finding the Equation of a Ellipse?

#### Incursion

How do you find the equation of a ellipse when given coordinates where the graph passes through?
Ex) Find the equation with center at the origin, vertex at (0,4) and passes through (√3, 2√3)?

EDIT: Found out I plugged in the A value (16 in this problem) in the wrong spot, making X some weird fraction. My next question is, how do you figure out what the major axis is in this equation, when they don't give the foci coordinates?

Last edited:

#### 11rdc11

How do you find the equation of a ellipse when given coordinates where the graph passes through?
Ex) Find the equation with center at the origin, vertex at (0,4) and passes through (√3, 2√3)?

EDIT: Found out I plugged in the A value (16 in this problem) in the wrong spot, making X some weird fraction. My next question is, how do you figure out what the major axis is in this equation, when they don't give the foci coordinates?
$$\displaystyle \frac{(\sqrt{3})^2}{a^2} + \frac{(2\sqrt{3})^2}{4^2}=1$$

• HallsofIvy

#### HallsofIvy

MHF Helper
How do you find the equation of a ellipse when given coordinates where the graph passes through?
Ex) Find the equation with center at the origin, vertex at (0,4) and passes through (√3, 2√3)?

EDIT: Found out I plugged in the A value (16 in this problem) in the wrong spot, making X some weird fraction. My next question is, how do you figure out what the major axis is in this equation, when they don't give the foci coordinates?
11rdc11's solution assumes the major and minor axes are along the x and y axes which you pretty much have to. There are an infinite number of solutions with the ellipse rotated relative to the x and y axes.