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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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}

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