Question

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

Answer 1

Solution

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 :

$\frac{(x-h)^2}{a^2}+\frac{(y-k)}{b^2}=1^2$

Therefore the equation of the ellipse is

$\frac{(x-4)}{16}^2+\frac{(y-0)^2}{1}=1$