What is the center 3x^2+7y^2-12x-28y+19=0 ?

The center 3x^2+7y^2-12x-28y+19=0 is (2,2)

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center 3x^2+7y^2-12x-28y+19=0

center

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

(2, 2)

Solution steps

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

Rewrite

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 7 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 2), a = 7, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 2), a = 7, b = 3

And the center is:

(2, 2)

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

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

What is the center 3x^2+7y^2-12x-28y+19=0 ?
The center 3x^2+7y^2-12x-28y+19=0 is (2,2)