Question

Write an equation in standard form of an ellipse that is 8 units high and 18 units wide. The center of the ellipse is (0,0)

Answer 1

Answer:

Equation of Ellipse in standard form is $\frac{(x-0)^2}{81}+\frac{(y-0)^2}{16}=1$

Step-by-step explanation:

Given: Center of ellipse is ( 0 , 0 )

Ellipse is 8 units high.

⇒ Length of minor axis = 8

⇒ b = $\frac{8}{2}=4$

Ellipse is 18 units wide.

⇒ Length of minor axis = 18

⇒ a = $\frac{18}{2}=9$

Standard equation of ellipse whose major axis ia x-axis is given by,

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

where ( h , k ) is coordinates of center.

⇒ Equation of Ellipse : $\frac{(x-0)^2}{9^2}+\frac{(y-0)^2}{4^2}=1$

                                      $\frac{x^2}{81}+\frac{y^2}{16}=1$

Therefore, Equation of Ellipse in standard form is $\frac{(x-0)^2}{81}+\frac{(y-0)^2}{16}=1$

Answer 2

Check the picture below.

$\bf \begin{cases} h=0\\ k=0\\ a=9\\ b=4 \end{cases}\implies \cfrac{(x-0)^2}{9^2}+\cfrac{(y-0)^2}{4^2}=1\implies \cfrac{x^2}{81}+\cfrac{y^2}{16}=1$