What is 9x^2+4y^2+36x-8y+4=0 ?

The solution to 9x^2+4y^2+36x-8y+4=0 is Ellipse with (h,k)=(-2,1),a=2,b=3

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9x^2+4y^2+36x-8y+4=0

9 x^{2} + 4 y^{2} + 36 x - 8 y + 4 = 0

(h, k) = (- 2, 1), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} + 36 x - 8 y + 4 = 0

Rewrite

9 x^{2} + 4 y^{2} + 36 x - 8 y + 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), b = 3, a = 2

7 x^{2} + 2 y^{2} = 14

4 x^{2} + 25 y^{2} - 6 x + 200 y + 304 = 0

(\frac{x + 4}{3})^{2} + (\frac{y + 4}{9})^{2} = (\frac{457}{81})^{2}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{36} = 1

16 x^{2} + y^{2} + 64 x + 4 y + 52 = 0

What is 9x^2+4y^2+36x-8y+4=0 ?
The solution to 9x^2+4y^2+36x-8y+4=0 is Ellipse with (h,k)=(-2,1),a=2,b=3