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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

4 x^{2} + 25 y^{2} - 8 x + 100 y + 4 = 0

\frac{2 ( x - 6 ) ^{2}}{3} + \frac{7 ( y + 4 ) ^{2}}{4} = 1

x^{(2)} + 2 y^{(2)} + 2 x - 20 y + 43 = 0

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} = 1

\frac{x ^{2}}{27} + \frac{y ^{2}}{36} = 1

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