What is 64x^2+81y^2-1024x+1458y+5473=0 ?

The solution to 64x^2+81y^2-1024x+1458y+5473=0 is Ellipse with (h,k)=(8,-9),a=9,b=8

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64x^2+81y^2-1024x+1458y+5473=0

64 x^{2} + 81 y^{2} - 1024 x + 1458 y + 5473 = 0

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

Solution steps

64 x^{2} + 81 y^{2} - 1024 x + 1458 y + 5473 = 0

Rewrite

64 x^{2} + 81 y^{2} - 1024 x + 1458 y + 5473 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x^{2} + 16 y^{2} - 10 x + 64 y + 73 = 0

1 = 4 x^{2} + y^{2}

x^{2} + 2 y^{2} = 30

4 x^{2} + 16 y^{2} + 32 y = 0

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 6 ) ^{2}}{121} = 1

What is 64x^2+81y^2-1024x+1458y+5473=0 ?
The solution to 64x^2+81y^2-1024x+1458y+5473=0 is Ellipse with (h,k)=(8,-9),a=9,b=8