What is 9x^2+4y^2-72x+108=0 ?

The solution to 9x^2+4y^2-72x+108=0 is Ellipse with (h,k)=(4,0),a=2,b=3

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9x^2+4y^2-72x+108=0

9 x^{2} + 4 y^{2} - 72 x + 108 = 0

(h, k) = (4, 0), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} - 72 x + 108 = 0

Rewrite

9 x^{2} + 4 y^{2} - 72 x + 108 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, 0), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, 0), b = 3, a = 2

\frac{x ^{2}}{144} + \frac{y ^{2}}{81} = 1

16 x^{2} - 96 x + 5 y^{2} + 10 y + 69 = 0

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

x^{2} + y^{2} \geq - 4 y

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 5 ) ^{2}}{3} = 1

What is 9x^2+4y^2-72x+108=0 ?
The solution to 9x^2+4y^2-72x+108=0 is Ellipse with (h,k)=(4,0),a=2,b=3