What is the center 5x^2+3y^2+30x+60y-45=0 ?

The center 5x^2+3y^2+30x+60y-45=0 is (-3,-10)

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

center

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

(- 3, - 10)

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{( 78 ) ^{2}} + \frac{( y - ( - 10 ) ) ^{2}}{( 130 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, - 10), a = 78, b = 130

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 10), b = 130, a = 78

And the center is:

(- 3, - 10)

\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

16 x^{2} + 4 y^{2} - 64 = 0

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

What is the center 5x^2+3y^2+30x+60y-45=0 ?
The center 5x^2+3y^2+30x+60y-45=0 is (-3,-10)