What is the eccentricity (8x^2)/1+(14y^2)/1 =122 ?

The eccentricity (8x^2)/1+(14y^2)/1 =122 is sqrt(3/7)

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eccentricity (8x^2)/1+(14y^2)/1 =122

eccentricity

\frac{8 x ^{2}}{1} + \frac{14 y ^{2}}{1} = 122

\frac{3}{7}

Solution steps

= \frac{a ^{2} - b ^{2}}{a}

Calculate ellipse properties

\frac{8 x ^{2}}{1} + \frac{14 y ^{2}}{1} = 122 :

Ellipse with center

(h, k) = (0, 0), a = \frac{61}{2}, b = \frac{61}{7}

= \frac{( \frac{61}{2} ) ^{2} - ( \frac{61}{7} ) ^{2}}{\frac{61}{2}}

\frac{( \frac{61}{2} ) ^{2} - ( \frac{61}{7} ) ^{2}}{\frac{61}{2}} = \frac{3}{7}

= \frac{3}{7}

\frac{( x - 4 ) ^{2}}{3} + \frac{y ^{2}}{9} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1

\frac{( x - 4 ) ^{2}}{5} + \frac{( y - 2 ) ^{2}}{4} = 1

49 x^{2} - 98 x + 64 y^{2} + 256 y - 2831 = 0

\frac{( x ^{2} )}{16} + \frac{( y ^{2} )}{25} = 1

What is the eccentricity (8x^2)/1+(14y^2)/1 =122 ?
The eccentricity (8x^2)/1+(14y^2)/1 =122 is sqrt(3/7)