What is the center x^2+4y^2-6x-16y+21=0 ?

The center x^2+4y^2-6x-16y+21=0 is (3,2)

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center x^2+4y^2-6x-16y+21=0

center

x^{2} + 4 y^{2} - 6 x - 16 y + 21 = 0

(3, 2)

Solution steps

x^{2} + 4 y^{2} - 6 x - 16 y + 21 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x - 16 y + 21 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

And the center is:

(3, 2)

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{100} = 1

36 x^{2} + 25 y^{2} = 900

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

25 x^{2} + 9 y^{2} - 150 x - 18 y + 9 = 0

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{4} = 1

What is the center x^2+4y^2-6x-16y+21=0 ?
The center x^2+4y^2-6x-16y+21=0 is (3,2)