What is x^2+9y^2+90y+189=0 ?

The solution to x^2+9y^2+90y+189=0 is Ellipse with (h,k)=(0,-5),a=6,b=2

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x^2+9y^2+90y+189=0

x^{2} + 9 y^{2} + 90 y + 189 = 0

(h, k) = (0, - 5), a = 6, b = 2

Solution steps

x^{2} + 9 y^{2} + 90 y + 189 = 0

Rewrite

x^{2} + 9 y^{2} + 90 y + 189 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 5), a = 6, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - 5), a = 6, b = 2

4 x^{2} + 36 y^{2} = 144

2 x - x^{2} - 4 y^{2} - 16 y - 1 \geq 0

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

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

6 x^{2} + y^{2} + 10 x = 0

What is x^2+9y^2+90y+189=0 ?
The solution to x^2+9y^2+90y+189=0 is Ellipse with (h,k)=(0,-5),a=6,b=2