What is 81x^2+9y^2=64 ?

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

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81x^2+9y^2=64

81 x^{2} + 9 y^{2} = 64

(h, k) = (0, 0), a = \frac{8}{9}, b = \frac{8}{3}

Solution steps

81 x^{2} + 9 y^{2} = 64

Rewrite

81 x^{2} + 9 y^{2} = 64

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{8}{9} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{8}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{8}{9}, b = \frac{8}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{8}{3}, a = \frac{8}{9}

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

\frac{x ^{2}}{25} + \frac{( y + 3 ) ^{2}}{49} = 1

9 x^{2} + 25 y^{2} = 225

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952

6 x^{2} + 8 y^{2} + 12 x - 32 y = 178

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