What is 9x^2+4y^2+18x+32y+37=0 ?

The solution to 9x^2+4y^2+18x+32y+37=0 is Ellipse with (h,k)=(-1,-4),a=2,b=3

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9x^2+4y^2+18x+32y+37=0

9 x^{2} + 4 y^{2} + 18 x + 32 y + 37 = 0

(h, k) = (- 1, - 4), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} + 18 x + 32 y + 37 = 0

Rewrite

9 x^{2} + 4 y^{2} + 18 x + 32 y + 37 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, - 4), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 4), b = 3, a = 2

\frac{x ^{2}}{100} + \frac{y ^{2}}{49} = 1

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

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

\frac{( x - 1 ) ^{2}}{7 ^{2}} + \frac{( y - 1 ) ^{2}}{3 ^{2}} = 1

\frac{( x - 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{25} = 1

What is 9x^2+4y^2+18x+32y+37=0 ?
The solution to 9x^2+4y^2+18x+32y+37=0 is Ellipse with (h,k)=(-1,-4),a=2,b=3