Question

Find the standard form of the equation of the ellipse satisfying the following conditions: endpoints of major axis (-5, 4) and (3, 4); endpoints of minor axis (-1, 1) and (-1, 7). Graph this conic, marking the center and vertices.

Answer 1

Step 1

Find the distance between the points in the major axis

`\begin{gathered} =√(\left(3-\left(-5\right)\right)^2+\left(4-4\right)^2) \\ =8 \end{gathered}`

Step 2

Find the distance between the points in the minor axis

`\begin{gathered} =√(\left(-1-\left(-1\right)\right)^2+\left(7-1\right)^2) \\ =6 \end{gathered}`

Step 3