What is 4x^2+36y^2+24x+432y=-1188 ?

The solution to 4x^2+36y^2+24x+432y=-1188 is Ellipse with (h,k)=(-3,-6),a=6,b=2

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4x^2+36y^2+24x+432y=-1188

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

(h, k) = (- 3, - 6), a = 6, b = 2

Solution steps

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

Rewrite

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{6 ^{2}} + \frac{( y - ( - 6 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, - 6), a = 6, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 6), a = 6, b = 2

\frac{( x - 3 ) ^{2}}{100} + \frac{( y + 4 ) ^{2}}{64} = 1

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

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

2 x^{2} + 3 y^{2} = 12

x^{2} + 4 y^{2} \leq 4

What is 4x^2+36y^2+24x+432y=-1188 ?
The solution to 4x^2+36y^2+24x+432y=-1188 is Ellipse with (h,k)=(-3,-6),a=6,b=2