What is x^{(2)}+4x+4y^{(2)}-6y+9=3 ?

The solution to x^{(2)}+4x+4y^{(2)}-6y+9=3 is Ellipse with (h,k)=(-2, 3/4),a= 1/2 ,b= 1/4

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x^{(2)}+4x+4y^{(2)}-6y+9=3

x^{(2)} + 4 x + 4 y^{(2)} - 6 y + 9 = 3

(h, k) = (- 2, \frac{3}{4}), a = \frac{1}{2}, b = \frac{1}{4}

Solution steps

x^{2} + 4 x + 4 y^{2} - 6 y + 9 = 3

Rewrite

x^{2} + 4 x + 4 y^{2} - 6 y + 9 = 3

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{1}{2} ) ^{2}} + \frac{( y - \frac{3}{4} ) ^{2}}{( \frac{1}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, \frac{3}{4}), a = \frac{1}{2}, b = \frac{1}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, \frac{3}{4}), a = \frac{1}{2}, b = \frac{1}{4}

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

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

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

16 x^{2} - 96 x + 9 y^{2} = 0

20 (x + 1)^{2} + 9 y^{2} = 180

What is x^{(2)}+4x+4y^{(2)}-6y+9=3 ?
The solution to x^{(2)}+4x+4y^{(2)}-6y+9=3 is Ellipse with (h,k)=(-2, 3/4),a= 1/2 ,b= 1/4