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} + 36 y^{2} = 49

\frac{( x + 1.23 ) ^{2}}{1.5 9 ^{2}} + \frac{y ^{2}}{1.0 1 ^{2}} = 1

\frac{x ^{2}}{12} + \frac{y ^{2}}{9} = 1

5 x^{2} + 6 y^{2} - 30 x - 24 y + 39 = 0

3 x^{(2)} + 7 y^{(2)} - 12 x - 28 y + 19 = 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