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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x^{2} + 4 y^{2} - 6 x + 40 y + 105 = 0

x, \frac{x ^{2}}{16} + \frac{Y ( x ) ^{2}}{9} = 1

9 (5.66 - 2) x^{2} + y^{2} = 36

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

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

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