What is (X^2)/(27)+(Y^2)/(36)=1 ?

The solution to (X^2)/(27)+(Y^2)/(36)=1 is Ellipse with (h,k)=(0,0),a=3sqrt(3),b=6

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(X^2)/(27)+(Y^2)/(36)=1

\frac{X ^{2}}{27} + \frac{Y ^{2}}{36} = 1

(h, k) = (0, 0), a = 33, b = 6

Solution steps

\frac{X ^{2}}{27} + \frac{Y ^{2}}{36} = 1

Rewrite

\frac{X ^{2}}{27} + \frac{Y ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( X - 0 ) ^{2}}{( 3 3 ) ^{2}} + \frac{( Y - 0 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 33, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 6, a = 33

x^{2} - 10 x + 4 y^{2} - 8 y = 5

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

\frac{x ^{2}}{2} + \frac{y ^{2}}{3} = 1

9 x^{2} + y^{2} + 18 x + 2 y + 1 = 0

2 x^{2} + 8 y^{2} = 25

What is (X^2)/(27)+(Y^2)/(36)=1 ?
The solution to (X^2)/(27)+(Y^2)/(36)=1 is Ellipse with (h,k)=(0,0),a=3sqrt(3),b=6