What is 5x^2+9y^2+30x-36y+36=0 ?

The solution to 5x^2+9y^2+30x-36y+36=0 is Ellipse with (h,k)=(-3,2),a=3,b=sqrt(5)

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5x^2+9y^2+30x-36y+36=0

5 x^{2} + 9 y^{2} + 30 x - 36 y + 36 = 0

(h, k) = (- 3, 2), a = 3, b = 5

Solution steps

5 x^{2} + 9 y^{2} + 30 x - 36 y + 36 = 0

Rewrite

5 x^{2} + 9 y^{2} + 30 x - 36 y + 36 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{3 ^{2}} + \frac{( y - 2 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 2), a = 3, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 2), a = 3, b = 5

x^{2} + 4 y^{2} - 1 = 0

x^{2} + 6 y^{2} = 3

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

3 x^{2} + 3 y^{2} - 36 y = 0

4 x^{2} + 8 y^{2} - 4 x - 24 y - 13 = 0

What is 5x^2+9y^2+30x-36y+36=0 ?
The solution to 5x^2+9y^2+30x-36y+36=0 is Ellipse with (h,k)=(-3,2),a=3,b=sqrt(5)