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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

9 x^{2} + 25 y^{2} + 18 x + 100 y - 116 = 0

\frac{( x ^{2} )}{4} + \frac{( y ^{2} )}{9} = 1

x^{(2)} + 4 x + 4 y^{(2)} - 6 y + 9 = 3

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

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