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

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

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

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

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

Solution steps

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

Rewrite

4 y^{2} + 9 x^{2} - 24 y - 72 x + 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} - 8 x + y^{2} + 6 y = 3

(x + 4)^{2} + (\frac{y - 41}{2})^{2} = \frac{421}{4}

\frac{x ^{2}}{4900} + \frac{y ^{2}}{2500} = 1

x^{2} + y^{2} - \frac{21}{8} x + \frac{19}{4} - \frac{525}{8} = 0

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

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