What is 4x^2-48x+9y^2+72y+144=0 ?

The solution to 4x^2-48x+9y^2+72y+144=0 is Ellipse with (h,k)=(6,-4),a=6,b=4

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4x^2-48x+9y^2+72y+144=0

4 x^{2} - 48 x + 9 y^{2} + 72 y + 144 = 0

(h, k) = (6, - 4), a = 6, b = 4

Solution steps

4 x^{2} - 48 x + 9 y^{2} + 72 y + 144 = 0

Rewrite

4 x^{2} - 48 x + 9 y^{2} + 72 y + 144 = 0

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, - 4), a = 6, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (6, - 4), a = 6, b = 4

\frac{( x - 2.22 ) ^{2}}{2.54} + \frac{y ^{2}}{1.11} = 2

25 x^{2} + 16 y^{2} - 100 x - 64 y - 236 = 0

12 x - 5 y + 10 x^{2} + 25 = \frac{- ( 100 y ^{2} )}{10 + 3}

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{36} = 1

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

What is 4x^2-48x+9y^2+72y+144=0 ?
The solution to 4x^2-48x+9y^2+72y+144=0 is Ellipse with (h,k)=(6,-4),a=6,b=4