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

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

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

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

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

Solution steps

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

Rewrite

9 x^{2} - 36 x + 25 y^{2} + 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

\frac{x ^{2}}{12} + \frac{y ^{2}}{144} = \frac{y}{12}

2 x^{2} + 5 y^{2} - 6 x - 2 y + 4 = 0

9 x^{2} + 36 x + 4 y^{2} - 24 y + 36 = 0

\frac{( x - 1 ) ^{2}}{3} + \frac{( y - 1 ) ^{2}}{25} = 1

\frac{( x - 4 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{36} = 1

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