Question

Write the equation of a vertical ellipse with a center of (5,-6) with a major axis of 3 and a minor axis of 2

Answer 1

Given:

Center of the ellipse (5,-6)

Major axis = 3

Minor axis = 2

Find-: Equation of ellipse.

Sol:

The general equation of the vertical ellipse is:

`((x-h)^2)/(b^2)+((y-k)^2)/(a^2)=1`

Where,

`\begin{gathered} \text{ Center = }(h,k) \\ \\ \text{ Major axis = 2a} \\ \\ \text{ Minor axis = 2b} \end{gathered}`

So, value of "a" , "b" is:

`\begin{gathered} \text{ Major axis = 3} \\ \\ 2a=3 \\ \\ a=(3)/(2) \end{gathered}`

Minor axis is:

`\begin{gathered} 2b=2 \\ \\ b=(2)/(2) \\ \\ b=1 \end{gathered}`

So equation become:

`\begin{gathered} ((x-h)^2)/(b^2)+((y-k)^2)/(a^2)=1 \\ \\ ((x-5)^2)/(1^2)+((y-(-6))^2)/(((3)/(2))^2)=1 \\ \\ ((x-5)^2)/(1)+((y+6)^2)/((9)/(4))=1 \end{gathered}`

Final equation of ellipse is

`\begin{gathered} ((x-5)^2)/(1)+((y+6)^2)/((9)/(4))=1 \\ \\ (x-5)^2+(4(y+6)^2)/(9)=1 \end{gathered}`