What is 4x^2+32x+9y^2+36y+64=0 ?

The solution to 4x^2+32x+9y^2+36y+64=0 is Ellipse with (h,k)=(-4,-2),a=3,b=2

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4x^2+32x+9y^2+36y+64=0

4 x^{2} + 32 x + 9 y^{2} + 36 y + 64 = 0

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

Solution steps

4 x^{2} + 32 x + 9 y^{2} + 36 y + 64 = 0

Rewrite

4 x^{2} + 32 x + 9 y^{2} + 36 y + 64 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{x ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{10} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{64} = 1

4 x^{2} + 3 y^{2} - 5 x + 2 y + 1 = 0

36 - 9 x^{2} - 4 y^{2} > 0

What is 4x^2+32x+9y^2+36y+64=0 ?
The solution to 4x^2+32x+9y^2+36y+64=0 is Ellipse with (h,k)=(-4,-2),a=3,b=2