What is (x^2)/4+(3x)/2+9y^2-18y+9=0 ?

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

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(x^2)/4+(3x)/2+9y^2-18y+9=0

\frac{x ^{2}}{4} + \frac{3 x}{2} + 9 y^{2} - 18 y + 9 = 0

(h, k) = (- 3, 1), a = 3, b = \frac{1}{2}

Solution steps

\frac{x ^{2}}{4} + \frac{3 x}{2} + 9 y^{2} - 18 y + 9 = 0

Rewrite

\frac{x ^{2}}{4} + \frac{3 x}{2} + 9 y^{2} - 18 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 3, b = \frac{1}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), a = 3, b = \frac{1}{2}

\frac{x ^{2}}{4} + \frac{z ^{2}}{16} = 4

\frac{( x - 2 ) ^{2}}{100} + \frac{y ^{2}}{36} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{49} = 1

\frac{( x - 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{16} = 1

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

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