What is 9x^2+25y^2+36x+150y+36=0 ?

The solution to 9x^2+25y^2+36x+150y+36=0 is Ellipse with (h,k)=(-2,-3),a=5,b=3

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9x^2+25y^2+36x+150y+36=0

9 x^{2} + 25 y^{2} + 36 x + 150 y + 36 = 0

(h, k) = (- 2, - 3), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} + 36 x + 150 y + 36 = 0

Rewrite

9 x^{2} + 25 y^{2} + 36 x + 150 y + 36 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 3), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 3), a = 5, b = 3

16 x^{2} + 25 y^{2} - 224 x - 150 y + 1009 = 400

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

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

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

x^{2} - 8 x + 16 y^{2} - 2 y + 4 = 625

What is 9x^2+25y^2+36x+150y+36=0 ?
The solution to 9x^2+25y^2+36x+150y+36=0 is Ellipse with (h,k)=(-2,-3),a=5,b=3