Question

Find the standard form of the equation of the ellipse satisfying the given conditions.Endpoints of major axis: (4,12) and (4,0)Endpoints of minor axis: (8,6) and (0,6)

Answer 1

The Standard form of the ellipse is given as,

`((x-a)^2)/(a^2)+\text{ }((y-b)^2)/(b^2)\text{ = 1}`

The length of the major axis is given as,

`\begin{gathered} 2a\text{ = 8} \\ a\text{ = }(8)/(2) \\ a\text{ = 4} \end{gathered}`

The length of the minor axis is given as,

`\begin{gathered} 2b\text{ = 12} \\ b\text{ = }(12)/(2) \\ b\text{ = 6} \end{gathered}`

Therefore the required equation is calculated as,

`\begin{gathered} ((x-4)^2)/(4^2)\text{ + }((y-6)^2)/(6^2)\text{ = 1} \\ \frac{(x-4)^2}{16^{}}\text{ + }\frac{(y-6)^2}{36^{}}\text{ = 1} \end{gathered}`