What is 9x^2-18x+4y^2-27=0 ?

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

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9x^2-18x+4y^2-27=0

9 x^{2} - 18 x + 4 y^{2} - 27 = 0

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

Solution steps

9 x^{2} - 18 x + 4 y^{2} - 27 = 0

Rewrite

9 x^{2} - 18 x + 4 y^{2} - 27 = 0

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

4 x^{2} + 25 y^{2} + 8 x = 96

(\frac{x ^{2}}{16}) + (\frac{y ^{2}}{25}) = 1

\frac{( x + 4 ) ^{2}}{6 ^{2}} + \frac{( y + 6 ) ^{2}}{7 ^{2}} = 1

X^{2} + 4 Y^{2} - 6 X - 16 Y + 21 = 0

(5 p + 3 q) 2 = 25 p^{2} + 9 q^{2}

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