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

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

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

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

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

Solution steps

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

Rewrite

4 x^{2} + 9 y^{2} - 48 x + 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

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