Question

What are the endpoints of the major axis and minor axis of the ellipse?

Answer 1

Given:

`((x-2)^2)/(36)+((y+3)^2)/(24)=1`

Required:

Find the endpoints of the major axis and minor axis of the ellipse.

Step-by-step explanation:

The standard equation of the ellipse is:

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

Where h and k are the centers of the ellipse and a and b are the length of the axis.

Rewrite the given equation as:

`((x-2)^2)/((6)^2)+((y+3)^2)/((2√(6))^2)=1`

Compare the given equation with the standard equation we get

`\begin{gathered} h=2,\text{ k=-3} \\ a=6,\text{ b=2}√(6) \end{gathered}`

Since a>b so the coordinate x-axis will be a major axis and the y-axis will be a minor axis.

The coordinate of the major axis are:

`(h\pm a,k)=(2\pm6,-3)`

Take + sign

`(2+6,-3)=(8,-3)`

Take - sign

`(2-6,-3)=(-4,-3_)`

The coordinates of the minor axis are:

`(h,k\pm b)=(2,-3\pm2√(6))`

Take the + sign

`(2,-3+2√(6))`

Take the - sign

`(2,-3-2√(6))`

Final Answer:

The coordinates of the major axis are: (8,-3) and (-4,-3)

The coordinates of the minor axis are:

`(2,-3\pm2√(6))`