What is x^2-6x+4y^2+8y-3=0 ?

The solution to x^2-6x+4y^2+8y-3=0 is Ellipse with (h,k)=(3,-1),a=4,b=2

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x^2-6x+4y^2+8y-3=0

x^{2} - 6 x + 4 y^{2} + 8 y - 3 = 0

(h, k) = (3, - 1), a = 4, b = 2

Solution steps

x^{2} - 6 x + 4 y^{2} + 8 y - 3 = 0

Rewrite

x^{2} - 6 x + 4 y^{2} + 8 y - 3 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), a = 4, b = 2

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{25} = 1

2 x^{2} - 12 x + y^{2} + 6 y + 26 = 0

\frac{x ^{2}}{9} + \frac{y ^{2}}{49} = 1

2 x^{2} + y^{2} + 12 x - 6 y + 26 = 0

4 x^{2} + 9 y^{2} = 25

What is x^2-6x+4y^2+8y-3=0 ?
The solution to x^2-6x+4y^2+8y-3=0 is Ellipse with (h,k)=(3,-1),a=4,b=2