What is x^2+9y^2+6x-90y+225=0 ?

The solution to x^2+9y^2+6x-90y+225=0 is Ellipse with (h,k)=(-3,5),a=3,b=1

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x^2+9y^2+6x-90y+225=0

x^{2} + 9 y^{2} + 6 x - 90 y + 225 = 0

(h, k) = (- 3, 5), a = 3, b = 1

Solution steps

x^{2} + 9 y^{2} + 6 x - 90 y + 225 = 0

Rewrite

x^{2} + 9 y^{2} + 6 x - 90 y + 225 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 5), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 5), a = 3, b = 1

x^{2} = - 4 y

x^{2} + y^{2} + 10 x + 12 y + 25 = 0

x^{2} = 16 y

y^{2} = - 10 x

\frac{x ^{2}}{25} + \frac{y ^{2}}{25} = 1

What is x^2+9y^2+6x-90y+225=0 ?
The solution to x^2+9y^2+6x-90y+225=0 is Ellipse with (h,k)=(-3,5),a=3,b=1