What is 2x^2+3y^2-8x+6y-7=0 ?

The solution to 2x^2+3y^2-8x+6y-7=0 is Ellipse with (h,k)=(2,-1),a=3,b=sqrt(6)

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

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

(h, k) = (2, - 1), a = 3, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 1), a = 3, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), a = 3, b = 6

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

9 x^{2} + 4 y^{2} - 8 y - 32 = 0

What is 2x^2+3y^2-8x+6y-7=0 ?
The solution to 2x^2+3y^2-8x+6y-7=0 is Ellipse with (h,k)=(2,-1),a=3,b=sqrt(6)