What is 2x^2+3y^2+4x-5y-6=0 ?

The solution to 2x^2+3y^2+4x-5y-6=0 is Ellipse with (h,k)=(-1, 5/6),a=(11)/(2sqrt(6)),b= 11/6

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2x^2+3y^2+4x-5y-6=0

2 x^{2} + 3 y^{2} + 4 x - 5 y - 6 = 0

(h, k) = (- 1, \frac{5}{6}), a = \frac{11}{2 6}, b = \frac{11}{6}

Solution steps

2 x^{2} + 3 y^{2} + 4 x - 5 y - 6 = 0

Rewrite

2 x^{2} + 3 y^{2} + 4 x - 5 y - 6 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{11}{2 6} ) ^{2}} + \frac{( y - \frac{5}{6} ) ^{2}}{( \frac{11}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, \frac{5}{6}), a = \frac{11}{2 6}, b = \frac{11}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, \frac{5}{6}), a = \frac{11}{2 6}, b = \frac{11}{6}

What is 2x^2+3y^2+4x-5y-6=0 ?
The solution to 2x^2+3y^2+4x-5y-6=0 is Ellipse with (h,k)=(-1, 5/6),a=(11)/(2sqrt(6)),b= 11/6