What is 9x^2+18x+25y^2+150y+9=0 ?

The solution to 9x^2+18x+25y^2+150y+9=0 is Ellipse with (h,k)=(-1,-3),a=5,b=3

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9x^2+18x+25y^2+150y+9=0

9 x^{2} + 18 x + 25 y^{2} + 150 y + 9 = 0

(h, k) = (- 1, - 3), a = 5, b = 3

Solution steps

9 x^{2} + 18 x + 25 y^{2} + 150 y + 9 = 0

Rewrite

9 x^{2} + 18 x + 25 y^{2} + 150 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, - 3), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 3), a = 5, b = 3

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

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{4} = 1

9 x^{2} + 5 y^{2} + 89 x - 60 y = 120

\frac{x ^{2}}{25} + \frac{y ^{2}}{81} = 1

\frac{x}{\frac{x ^{2}}{64} + \frac{y ^{2}}{9}} = 1

What is 9x^2+18x+25y^2+150y+9=0 ?
The solution to 9x^2+18x+25y^2+150y+9=0 is Ellipse with (h,k)=(-1,-3),a=5,b=3