What is 4x^2+9y^2-24x+72y+144=0 ?

The solution to 4x^2+9y^2-24x+72y+144=0 is Ellipse with (h,k)=(3,-4),a=3,b=2

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4x^2+9y^2-24x+72y+144=0

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

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

Solution steps

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

Rewrite

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + 9 y^{2} + 24 x + 18 y + 9 = 0

x^{2} + 5 y^{2} = 2

x^{2} + 4 y^{2} + 2 x + 8 y + 1 = 0

25 x^{2} + 16 y^{2} + 150 x - 128 y - 1119 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{16} = 1

What is 4x^2+9y^2-24x+72y+144=0 ?
The solution to 4x^2+9y^2-24x+72y+144=0 is Ellipse with (h,k)=(3,-4),a=3,b=2