What is 3x^2+12y^2-6x-48y+33=0 ?

The solution to 3x^2+12y^2-6x-48y+33=0 is Ellipse with (h,k)=(1,2),a=sqrt(6),b=sqrt(3/2)

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3x^2+12y^2-6x-48y+33=0

3 x^{2} + 12 y^{2} - 6 x - 48 y + 33 = 0

(h, k) = (1, 2), a = 6, b = \frac{3}{2}

Solution steps

3 x^{2} + 12 y^{2} - 6 x - 48 y + 33 = 0

Rewrite

3 x^{2} + 12 y^{2} - 6 x - 48 y + 33 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 6, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 6, b = \frac{3}{2}

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

2 x - x^{2} - 4 y^{2} - 16 y - 1 > 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{64} = 1

25 x^{2} + 16 y^{2} - 50 x + 64 y - 311 = 0

\frac{x ^{2}}{9} + \frac{y ^{2}}{8} = 1

What is 3x^2+12y^2-6x-48y+33=0 ?
The solution to 3x^2+12y^2-6x-48y+33=0 is Ellipse with (h,k)=(1,2),a=sqrt(6),b=sqrt(3/2)