What is (y^2)/(81)+((x+5)^2)/(27)=1 ?

The solution to (y^2)/(81)+((x+5)^2)/(27)=1 is Ellipse with (h,k)=(-5,0),a=3sqrt(3),b=9

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(y^2)/(81)+((x+5)^2)/(27)=1

\frac{y ^{2}}{81} + \frac{( x + 5 ) ^{2}}{27} = 1

(h, k) = (- 5, 0), a = 33, b = 9

Solution steps

\frac{y ^{2}}{81} + \frac{( x + 5 ) ^{2}}{27} = 1

Rewrite

\frac{y ^{2}}{81} + \frac{( x + 5 ) ^{2}}{27} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( 3 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, 0), a = 33, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 5, 0), b = 9, a = 33

x^{2} + 10 x + 3 y^{2} + 10 y = 14

\frac{x ^{2}}{12} + \frac{y ^{2}}{12 - 16} = 1

22 x^{2} + 4 y^{2} = 1

x^{2} + 4 y^{2} + 10 x + 9 y - 10 = 0

16 x^{2} + 81 y^{2} = 81

What is (y^2)/(81)+((x+5)^2)/(27)=1 ?
The solution to (y^2)/(81)+((x+5)^2)/(27)=1 is Ellipse with (h,k)=(-5,0),a=3sqrt(3),b=9