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)

5 x^{2} + 2 y^{2} = 50

\frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

x^{2} + \frac{y ^{2}}{16} = 1

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

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)