What is 1x^2+4y^2+8x+9y-9=0 ?

The solution to 1x^2+4y^2+8x+9y-9=0 is Ellipse with (h,k)=(-4,-9/8),a=(sqrt(481))/4 ,b=(sqrt(481))/8

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1x^2+4y^2+8x+9y-9=0

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

(h, k) = (- 4, - \frac{9}{8}), a = \frac{481}{4}, b = \frac{481}{8}

Solution steps

1 \cdot x^{2} + 4 y^{2} + 8 x + 9 y - 9 = 0

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{( \frac{481}{4} ) ^{2}} + \frac{( y - ( - \frac{9}{8} ) ) ^{2}}{( \frac{481}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, - \frac{9}{8}), a = \frac{481}{4}, b = \frac{481}{8}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, - \frac{9}{8}), a = \frac{481}{4}, b = \frac{481}{8}

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

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - 2 ) ^{2}}{9} = 1

16 x^{2} - 64 x + 25 y^{2} + 150 y = 111

\frac{x ^{2}}{100} + \frac{y ^{2}}{25} = 1

4 x^{2} + 2 y^{2} = 1

What is 1x^2+4y^2+8x+9y-9=0 ?
The solution to 1x^2+4y^2+8x+9y-9=0 is Ellipse with (h,k)=(-4,-9/8),a=(sqrt(481))/4 ,b=(sqrt(481))/8