What is x^2+4y^2-6x-32y+72=0 ?

The solution to x^2+4y^2-6x-32y+72=0 is Ellipse with (h,k)=(3,4),a=1,b= 1/2

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x^2+4y^2-6x-32y+72=0

x^{2} + 4 y^{2} - 6 x - 32 y + 72 = 0

(h, k) = (3, 4), a = 1, b = \frac{1}{2}

Solution steps

x^{2} + 4 y^{2} - 6 x - 32 y + 72 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x - 32 y + 72 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 4), a = 1, b = \frac{1}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 4), a = 1, b = \frac{1}{2}

(- y^{2}) = x^{2} + 12

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{16} = 1

\frac{x ^{2}}{580 0 ^{2}} + \frac{y ^{2}}{150 0 ^{2}} = 1

9 x^{2} + y^{2} - 54 x - 6 y + 81 = 0

x^{2} = \frac{4 - y ^{2}}{2}

What is x^2+4y^2-6x-32y+72=0 ?
The solution to x^2+4y^2-6x-32y+72=0 is Ellipse with (h,k)=(3,4),a=1,b= 1/2