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inessss [21]
3 years ago
14

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)

Mathematics
2 answers:
Kazeer [188]3 years ago
4 0

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

zhenek [66]3 years ago
3 0
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

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