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uestion 7of 10 Step 1 of 1ind the equation of the ellipse with the following properties. Express your answer in standard form.Centered at (-4, 4)Major axis of length 18 oriented verticallyMinor axis of length 4swer 2 Points

Uestion 7of 10 Step 1 Of 1ind The Equation Of The Ellipse With The Following Properties Express Your Answer In Standard FormCentered At 4 4Major Axis Of Length class=

Sagot :

Answer:[tex]\frac{(x+4)^{2}}{81}+\frac{(y-4)^{2}}{4}=1[/tex]Explanation:

The center of the ellipse, (h, k) = (-4, 4)

The length of the major axis = 18

The length of the semi-major axis, a = 18/2 = 9

The length of the minor axis = 4

The length of the semi minor axis, b = 4/2 = 2

The equation of the ellipse is calculated as shown below

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Substitute h = -4, k = 4, a = 9, and b = 2 into the equation

[tex]\begin{gathered} \frac{(x-(-4))^2}{9^2}+\frac{(y-4)^2}{2^2}=1 \\ \\ \frac{(x+4)^2}{81}+\frac{(y-4)^2}{4}=1 \end{gathered}[/tex]

Therefore, the equation of the ellipse is:

[tex]\frac{(x+4)^{2}}{81}+\frac{(y-4)^{2}}{4}=1[/tex]

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