What is 3x^2+2y^2-12x+6y-10=0 ?

The solution to 3x^2+2y^2-12x+6y-10=0 is Ellipse with (h,k)=(2,-3/2),a=sqrt(53/6),b=(sqrt(53))/2

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3x^2+2y^2-12x+6y-10=0

3 x^{2} + 2 y^{2} - 12 x + 6 y - 10 = 0

(h, k) = (2, - \frac{3}{2}), a = \frac{53}{6}, b = \frac{53}{2}

Solution steps

3 x^{2} + 2 y^{2} - 12 x + 6 y - 10 = 0

Rewrite

3 x^{2} + 2 y^{2} - 12 x + 6 y - 10 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{53}{6} ) ^{2}} + \frac{( y - ( - \frac{3}{2} ) ) ^{2}}{( \frac{53}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - \frac{3}{2}), a = \frac{53}{6}, b = \frac{53}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - \frac{3}{2}), b = \frac{53}{2}, a = \frac{53}{6}

4.14 x^{2} + 3.92 y^{2} - 41.82 x - 82.62 y + 78 = 0

36 x^{2} + 8 y^{2} = 98

(\frac{y}{8})^{2} + (\frac{x}{7})^{2} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{9} = 1

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{6} - 1 = 0

What is 3x^2+2y^2-12x+6y-10=0 ?
The solution to 3x^2+2y^2-12x+6y-10=0 is Ellipse with (h,k)=(2,-3/2),a=sqrt(53/6),b=(sqrt(53))/2