What is 9x^2-18x+4y^2=27 ?

The solution to 9x^2-18x+4y^2=27 is Ellipse with (h,k)=(1,0),a=2,b=3

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9x^2-18x+4y^2=27

9 x^{2} - 18 x + 4 y^{2} = 27

(h, k) = (1, 0), a = 2, b = 3

Solution steps

9 x^{2} - 18 x + 4 y^{2} = 27

Rewrite

9 x^{2} - 18 x + 4 y^{2} = 27

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 0), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 0), b = 3, a = 2

2 x^{2} + y^{2} - 4 x + 6 y + 3 = 0

25 x^{2} + 4 y^{2} - 250 x - 16 y + 541 = 0

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

10 x^{2} + 4 y^{2} - 8 x - 10 y - 12 = 0

What is 9x^2-18x+4y^2=27 ?
The solution to 9x^2-18x+4y^2=27 is Ellipse with (h,k)=(1,0),a=2,b=3