What is x^2+4y^2-6x+8y+9=0 ?

The solution to x^2+4y^2-6x+8y+9=0 is Ellipse with (h,k)=(3,-1),a=2,b=1

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x^2+4y^2-6x+8y+9=0

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

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

Solution steps

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

10 x^{2} + 4 y^{2} - 8 x - 10 y - 12 = 0

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

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

25 x^{2} + 36 y^{2} + 100 x + 72 y - 764 = 0

What is x^2+4y^2-6x+8y+9=0 ?
The solution to x^2+4y^2-6x+8y+9=0 is Ellipse with (h,k)=(3,-1),a=2,b=1