What is 9x^{(2)}+25y^{(2)}+18x+150y+9=0 ?

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

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

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

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

Solution steps

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

Rewrite

9 x^{2} + 25 y^{2} + 18 x + 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{y ^{2}}{4} + \frac{x ^{2}}{9} = 1

9 x^{2} + 25 y^{2} + 36 x - 200 y + 211 = 0

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

4 x^{2} + 6 y^{2} - 8 x + 4 y - 6 \geq 0

25 x^{2} + 4 y^{2} + 200 x - 8 y + 304 = 0

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