What is the center 36x^2+9y^2+48x-36y+43=0 ?

The center 36x^2+9y^2+48x-36y+43=0 is (-2/3 ,2)

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center 36x^2+9y^2+48x-36y+43=0

center

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

(- \frac{2}{3}, 2)

Solution steps

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

Rewrite

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- \frac{2}{3}, 2), a = \frac{1}{2}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{2}{3}, 2), b = 1, a = \frac{1}{2}

And the center is:

(- \frac{2}{3}, 2)

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

5 x^{2} + 3 y^{2} + 30 x + 60 y - 45 = 0

\frac{( x + 3 ) ^{2}}{49} + \frac{y ^{2}}{36} = 1

\frac{( x + 2 ) ^{2}}{81} + \frac{y ^{2}}{36} = 1

25 x^{2} + 16 y^{2} < 400

What is the center 36x^2+9y^2+48x-36y+43=0 ?
The center 36x^2+9y^2+48x-36y+43=0 is (-2/3 ,2)