What is the eccentricity ((x+4)^2)/(25/4)+(y-6)^2=1 ?

The eccentricity ((x+4)^2)/(25/4)+(y-6)^2=1 is (sqrt(21))/5

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eccentricity ((x+4)^2)/(25/4)+(y-6)^2=1

eccentricity

\frac{( x + 4 ) ^{2}}{\frac{25}{4}} + (y - 6)^{2} = 1

\frac{21}{5}

Solution steps

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

Calculate ellipse properties

\frac{( x + 4 ) ^{2}}{\frac{25}{4}} + (y - 6)^{2} = 1 :

Ellipse with center

(h, k) = (- 4, 6), a = \frac{5}{2}, b = 1

= \frac{( \frac{5}{2} ) ^{2} - 1 ^{2}}{\frac{5}{2}}

\frac{( \frac{5}{2} ) ^{2} - 1 ^{2}}{\frac{5}{2}} = \frac{21}{5}

= \frac{21}{5}

7 x^{2} + 9 y^{2} = 63

4 xx + 9 yy = 36

25 x^{2} - 12 y + y^{2} - 26 y = - 11

5 x^{2} + 2 y^{2} = 50

6 x^{2} + 10 y^{2} = 60

What is the eccentricity ((x+4)^2)/(25/4)+(y-6)^2=1 ?
The eccentricity ((x+4)^2)/(25/4)+(y-6)^2=1 is (sqrt(21))/5