# math

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Find the vertices, foci, and eccentricity of the ellipse.
64x^2 + 81y^2 = 5184

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We have to bring in into form: x^2/a^2+y^2/b^2=1. So dividing everyone by 5184 and simplifying: x^2/81+y^2/64=1
so; x^2/9^2+y^2/8^2=1 therefore a=9 and b=8. Vertices on x-axis (9,0)&(-9,0) on y-axis (0,8)&(0,-8). foci: (c,0)&(-c,0) where c^2=a^2-b^2 so c^2=81-64=17 so c= sqrt71. Locus: (sqrt71,0)&(-sqrt71,0)
eccentricity e=c/a so e= sqrt71/9

try to do the others yourself

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