What is the center 9x^2+49y^2+18x+294y-9=0 ?

The center 9x^2+49y^2+18x+294y-9=0 is (-1,-3)

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center 9x^2+49y^2+18x+294y-9=0

center

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

(- 1, - 3)

Solution steps

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

Rewrite

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( 51 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{3 51}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

And the center is:

(- 1, - 3)

\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

4 x^{2} + y^{2} - 5 = 0

\frac{x ^{2}}{81} + \frac{y ^{2}}{64} = 1

\frac{( x + 3 ) ^{2}}{16} + \frac{( y + 4 ) ^{2}}{9} = 1

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{36} = 1

What is the center 9x^2+49y^2+18x+294y-9=0 ?
The center 9x^2+49y^2+18x+294y-9=0 is (-1,-3)