What is 6x^2+144y^2=864 ?

The solution to 6x^2+144y^2=864 is Ellipse with (h,k)=(0,0),a=12,b=sqrt(6)

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6x^2+144y^2=864

6 x^{2} + 144 y^{2} = 864

(h, k) = (0, 0), a = 12, b = 6

Solution steps

6 x^{2} + 144 y^{2} = 864

Rewrite

6 x^{2} + 144 y^{2} = 864

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 2 ^{2}} + \frac{( y - 0 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 12, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 12, b = 6

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

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

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

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

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

What is 6x^2+144y^2=864 ?
The solution to 6x^2+144y^2=864 is Ellipse with (h,k)=(0,0),a=12,b=sqrt(6)