Question #270952

Use the information provided to write the standard form equation of ellipse. Then sketch



the graph.



Foci: (-10, 16), (-10,-8)



Endpoints of major axis: (-10, 17),(-10,-9)

1
Expert's answer
2021-11-25T13:38:04-0500

Vertices: (10,17),(10,9)(-10, 17),(-10,-9)

Major axis is vertical, length =17(9)=26=2a=>a=13=17-(-9)=26=2a=>a=13


1713=4=9(13)17-13=4=-9-(-13)

Center: (10,4)(-10, 4)


Foci: (10,16),(10,8)(-10, 16), (-10,-8)


2c=16(8)=24=>c=122c=16-(-8)=24=>c=12

c2=a2b2=>b2=132122=25=>b=5c^2=a^2-b^2=>b^2=13^2-12^2=25=>b=5

The equation of the ellipse


(y4)2169+(x+10)225=1\dfrac{(y-4)^2}{169}+\dfrac{(x+10)^2}{25}=1

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