Question #252861

Find the equation of the ellipse in standard form whose Foci is (2,7) and (-2,7) and the length of the major axis is 6


1
Expert's answer
2021-10-20T00:10:02-0400

The center is located midway between the vertices on the major axis:

center=((2+(2)2,7+72)=(0,7)(\frac{(2+(-2)}{2},\frac{7+7}{2})=(0,7)

length of major axis= 6=2a

    a=3\implies a=3

c2=a2b2c=2,a=322=32b2b2=94=5b=5c^2=a^2-b^2\\ c=2,a=3\\ 2^2=3^2-b^2\\ b^2=9-4=5\\ b=\sqrt 5

The standard form equation of the ellipse is (xh)2a2+(yk)2b2=1\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1

x29+(y7)25=1\frac{x^2}{9}+\frac{(y-7)^2}{5}=1




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