What is 9x^2+6y^2=54 ?

The solution to 9x^2+6y^2=54 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=3

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9x^2+6y^2=54

9 x^{2} + 6 y^{2} = 54

(h, k) = (0, 0), a = 6, b = 3

Solution steps

9 x^{2} + 6 y^{2} = 54

Rewrite

9 x^{2} + 6 y^{2} = 54

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 3, a = 6

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

x^{2} + 9 y^{2} - 2 x - 72 y + 136 = 0

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

\frac{x ^{2}}{100} + \frac{y ^{2}}{25} = 16

\frac{( x + 5 ) ^{2}}{25} + \frac{( y + 4 ) ^{2}}{9} = 1

What is 9x^2+6y^2=54 ?
The solution to 9x^2+6y^2=54 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=3