What is 9(x-6)^2+64(y-4)^2=576 ?

The solution to 9(x-6)^2+64(y-4)^2=576 is Ellipse with (h,k)=(6,4),a=8,b=3

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9(x-6)^2+64(y-4)^2=576

9 (x - 6)^{2} + 64 (y - 4)^{2} = 576

(h, k) = (6, 4), a = 8, b = 3

Solution steps

9 (x - 6)^{2} + 64 (y - 4)^{2} = 576

Rewrite

9 (x - 6)^{2} + 64 (y - 4)^{2} = 576

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{8 ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, 4), a = 8, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (6, 4), a = 8, b = 3

6 x + 3 y \cdot 2 = 4 + 2 x^{2} + 5 y^{2}

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

25 x^{2} + 64 y^{2} = 1600

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

\frac{( y - 8 ) ^{2}}{40} + \frac{( x + 10 ) ^{2}}{211} = 1

What is 9(x-6)^2+64(y-4)^2=576 ?
The solution to 9(x-6)^2+64(y-4)^2=576 is Ellipse with (h,k)=(6,4),a=8,b=3