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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x, 4 x^{2} = 20 x - p (x)^{2} + 4

3 x^{2} + 4 y^{2} - 12 x + 16 y + 16 = 0

3 x^{2} + 5 y^{2} + 6 x - 10 y + 7 = 0

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

4 x^{2} + y^{2} - 16 x + 8 y - 20 = 0

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