Question

Writing an equation of an ellipse given the center and endpoint of an axis and the length of the other access

Answer 1

Writing an equation of an ellipse given the center and endpoint of an axis

Let center C ; C(h=4; k= 0)

Let the length of its major axis AA’=2a=8 ; a=4

Let the length of its minor axix BB’=2b=?

B(4 ; 0) ; C(4 ; - 1) ; BC=b

`\begin{gathered} b^2=(4-4)^2+(0--1)^2 \\ b^2=0+1^2 \\ b=1 \end{gathered}`

The equation of ellipse in standard form when it is horizontal is :

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

Therefore the equation of the ellipse is

`((x-4))/(16)^2+((y-0)^2)/(1)=1`