What is 64x^2+81y^2-1152x-486y+729=0 ?

The solution to 64x^2+81y^2-1152x-486y+729=0 is Ellipse with (h,k)=(9,3),a=9,b=8

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64x^2+81y^2-1152x-486y+729=0

64 x^{2} + 81 y^{2} - 1152 x - 486 y + 729 = 0

(h, k) = (9, 3), a = 9, b = 8

Solution steps

64 x^{2} + 81 y^{2} - 1152 x - 486 y + 729 = 0

Rewrite

64 x^{2} + 81 y^{2} - 1152 x - 486 y + 729 = 0

in the form of the standard ellipse equation

\frac{( x - 9 ) ^{2}}{9 ^{2}} + \frac{( y - 3 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (9, 3), a = 9, b = 8

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (9, 3), a = 9, b = 8

4 = x^{2} + 4 y^{2}

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

2 x^{2} + (y - 1)^{2} \leq 3

\frac{( x + 1 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{4} = 1

3 x^{2} + y^{2} - 22 x + 22 y = 6

What is 64x^2+81y^2-1152x-486y+729=0 ?
The solution to 64x^2+81y^2-1152x-486y+729=0 is Ellipse with (h,k)=(9,3),a=9,b=8