What is 9(5.66-2)x^2+y^2=36 ?

The solution to 9(5.66-2)x^2+y^2=36 is Ellipse with (h,k)=(0,0),a=1.04541…,b=6

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9(5.66-2)x^2+y^2=36

9 (5.66 - 2) x^{2} + y^{2} = 36

(h, k) = (0, 0), a = 1.04541 \dots, b = 6

Solution steps

9 (5.66 - 2) x^{2} + y^{2} = 36

Rewrite

9 (5.66 - 2) x^{2} + y^{2} = 36

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1.04541 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1.04541 \dots, 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 = 1.04541 \dots

9 x^{2} - 36 x + 25 y^{2} + 150 y + 36 = 0

\frac{x ^{2}}{12} + \frac{y ^{2}}{144} = \frac{y}{12}

2 x^{2} + 5 y^{2} - 6 x - 2 y + 4 = 0

9 x^{2} + 36 x + 4 y^{2} - 24 y + 36 = 0

\frac{( x - 1 ) ^{2}}{3} + \frac{( y - 1 ) ^{2}}{25} = 1

What is 9(5.66-2)x^2+y^2=36 ?
The solution to 9(5.66-2)x^2+y^2=36 is Ellipse with (h,k)=(0,0),a=1.04541…,b=6