What is 2x^2+3y^2+8x+10y-2=0 ?

The solution to 2x^2+3y^2+8x+10y-2=0 is Ellipse with (h,k)=(-2,-5/3),a=sqrt(55/6),b=(sqrt(55))/3

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2x^2+3y^2+8x+10y-2=0

2 x^{2} + 3 y^{2} + 8 x + 10 y - 2 = 0

(h, k) = (- 2, - \frac{5}{3}), a = \frac{55}{6}, b = \frac{55}{3}

Solution steps

2 x^{2} + 3 y^{2} + 8 x + 10 y - 2 = 0

Rewrite

2 x^{2} + 3 y^{2} + 8 x + 10 y - 2 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{55}{6} ) ^{2}} + \frac{( y - ( - \frac{5}{3} ) ) ^{2}}{( \frac{55}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - \frac{5}{3}), a = \frac{55}{6}, b = \frac{55}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - \frac{5}{3}), a = \frac{55}{6}, b = \frac{55}{3}

2 x^{2} + 3 y^{2} - 8 x + 6 y - 7 = 0

530 x^{2} + 785 y^{2} + 1060 x - 1570 y = 24650

3 x^{2} + 2 y^{2} \leq 6

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{25} = 1

2 x^{2} + 10 y^{2} = 20

What is 2x^2+3y^2+8x+10y-2=0 ?
The solution to 2x^2+3y^2+8x+10y-2=0 is Ellipse with (h,k)=(-2,-5/3),a=sqrt(55/6),b=(sqrt(55))/3