Mathematics: Write the equation of an ellipse with intercepts (-2,0), (2,0), (0,4), (0,-4). then find the foci. write the answer as square root (no decimals) show work.

Write the equation of an ellipse with intercepts

Ответ:

Peggy1621

17.01.2022

First, the major axis of the ellipse is vertical. The standard form of the equation of a vertical ellipse is $\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1$ . Here we can see that b=2

and

. So the equation is $\dfrac{x^2}{4}+\dfrac{y^2}{16}=1$ . To find the foci, use $c^2=a^2-b^2= 16-4\\ \implies c=\sqrt{12}=2\sqrt{3}$ . The foci will be located on the axis the vertexes are on, so that makes the coordinates of the foci $(0,\pm 2\sqrt{3})$ .

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Ответ:

risarod6106

29.05.2023

Mathematics

y = 5x + 2

Step-by-step explanation:

x=0 y=2 => b=2

x = 1 y = 7 b=2 => m =5

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Write the equation of an ellipse with intercepts (-2,0), (2,0), (0,4), (0,-4). then find the foci. write the answer as square root (no decimals) show work.

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