Question

7. 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).-164 32481216

Answer 1

The information given can be represented in the diagram below.

This shows that the ellipse cuts across both sides of the x axis at -9 and +9 to give 18 units wide and the y axis at -4 and 4 to give 8 units high.

The equation of the ellipse is

`\begin{gathered} (x^2)/(a^2)+(y^2)/(b^2)=1 \\ \end{gathered}`

"a" is the distance between the origin and where the ellipse cuts across the x axis.

"b" is the distance between the origin and where the ellipse cuts across the y axis.

Therefore, a=9 and b=4

Hence, the equation of the ellipse gives;

`\begin{gathered} (x^2)/(9^2)+(y^2)/(4^2)=1 \\ \frac{x^2}{81^{}}+\frac{y^2}{16^{}}=1 \end{gathered}`

In conclusion, the answer is B