What is x^2+4y^2-6x+12y-11=0 ?

The solution to x^2+4y^2-6x+12y-11=0 is Ellipse with (h,k)=(3,-3/2),a=sqrt(29),b=(sqrt(29))/2

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x^2+4y^2-6x+12y-11=0

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

(h, k) = (3, - \frac{3}{2}), a = 29, b = \frac{29}{2}

Solution steps

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 29 ) ^{2}} + \frac{( y - ( - \frac{3}{2} ) ) ^{2}}{( \frac{29}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - \frac{3}{2}), a = 29, b = \frac{29}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - \frac{3}{2}), a = 29, b = \frac{29}{2}

\frac{( x ^{2} )}{( 16 )} + \frac{( y ^{2} )}{( 25 )} = 1

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

\frac{( x - 7 ) ^{2}}{81} + \frac{( y ) ^{2}}{9} = 1

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

x (100 - 3 x) + y (192 - 6 y) = 0

What is x^2+4y^2-6x+12y-11=0 ?
The solution to x^2+4y^2-6x+12y-11=0 is Ellipse with (h,k)=(3,-3/2),a=sqrt(29),b=(sqrt(29))/2