What is 2x^2+3y^2-8x+6y+5=0 ?

The solution to 2x^2+3y^2-8x+6y+5=0 is Ellipse with (h,k)=(2,-1),a=sqrt(3),b=sqrt(2)

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2x^2+3y^2-8x+6y+5=0

2 x^{2} + 3 y^{2} - 8 x + 6 y + 5 = 0

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

Solution steps

2 x^{2} + 3 y^{2} - 8 x + 6 y + 5 = 0

Rewrite

2 x^{2} + 3 y^{2} - 8 x + 6 y + 5 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{1} = 1

25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

5 x^{2} + 7 y^{2} = 35

(\frac{x ^{2}}{a}) + (\frac{y ^{2}}{b}) = 1

What is 2x^2+3y^2-8x+6y+5=0 ?
The solution to 2x^2+3y^2-8x+6y+5=0 is Ellipse with (h,k)=(2,-1),a=sqrt(3),b=sqrt(2)