ANSWER FAST! TIMED TEST! Find the equation of the ellipse with foci at (8,0) and (-8,0) and a vertex at (12,0)

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ANSWER FAST! TIMED TEST!

Find the equation of the ellipse with foci at (8,0) and (-8,0) and a vertex at (12,0)

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Autumn 3 weeks 2022-01-03T08:26:24+00:00 1 Answer 0 views 0

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    2022-01-03T08:28:17+00:00

    Answer:

    \frac{x^2}{144}+\frac{y^2}{80}=1

    Step-by-step explanation:

    We want to find the equation of an ellipse with foci at (8,0) and (-8,0) and a vertex at (12,0)

    This is a horizontal ellipse with its center at the origin.

    The equation is of the form:

    \frac{x^2}{a^2}+\frac{y^2}{b^2}=1

    Since the vertex is at (0,12)——>a=12

    Since the foci is at (\pm8,0), we have c=8

    Using a^2-b^2=c^2

    We have  12^2-b^2=8^2

    b^2=12^2-8^2

    b^2=80

    Our equation now becomes:

    \frac{x^2}{12^2}+\frac{y^2}{80}=1

    Or

    \frac{x^2}{144}+\frac{y^2}{80}=1

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