What is x^2+2y^2+4x+18y-100=0 ?

The solution to x^2+2y^2+4x+18y-100=0 is Ellipse with (h,k)=(-2,-9/2),a=(17)/(sqrt(2)),b= 17/2

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x^2+2y^2+4x+18y-100=0

x^{2} + 2 y^{2} + 4 x + 18 y - 100 = 0

(h, k) = (- 2, - \frac{9}{2}), a = \frac{17}{2}, b = \frac{17}{2}

Solution steps

x^{2} + 2 y^{2} + 4 x + 18 y - 100 = 0

Rewrite

x^{2} + 2 y^{2} + 4 x + 18 y - 100 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{17}{2} ) ^{2}} + \frac{( y - ( - \frac{9}{2} ) ) ^{2}}{( \frac{17}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - \frac{9}{2}), a = \frac{17}{2}, b = \frac{17}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - \frac{9}{2}), a = \frac{17}{2}, b = \frac{17}{2}

4 x^{2} + 4 y^{2} + 16 y = 0

9 (x - 6)^{2} + 64 (y - 4)^{2} = 576

6 x + 3 y \cdot 2 = 4 + 2 x^{2} + 5 y^{2}

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

25 x^{2} + 64 y^{2} = 1600

What is x^2+2y^2+4x+18y-100=0 ?
The solution to x^2+2y^2+4x+18y-100=0 is Ellipse with (h,k)=(-2,-9/2),a=(17)/(sqrt(2)),b= 17/2