What is 9x^2+25y^2+36x-200y+211=0 ?

The solution to 9x^2+25y^2+36x-200y+211=0 is Ellipse with (h,k)=(-2,4),a=5,b=3

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9x^2+25y^2+36x-200y+211=0

9 x^{2} + 25 y^{2} + 36 x - 200 y + 211 = 0

(h, k) = (- 2, 4), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} + 36 x - 200 y + 211 = 0

Rewrite

9 x^{2} + 25 y^{2} + 36 x - 200 y + 211 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{5 ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 4), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 4), a = 5, b = 3

8 x^{2} + y^{2} + 4 y = 0

4 x^{2} + 6 y^{2} - 8 x + 4 y - 6 \geq 0

25 x^{2} + 4 y^{2} + 200 x - 8 y + 304 = 0

(x - 3)^{2} + 16 (y - 2)^{2} = 16

\frac{( 2 x + 1 ) ^{2}}{4} + \frac{( 3 y - 2 ) ^{2}}{16} = 1

What is 9x^2+25y^2+36x-200y+211=0 ?
The solution to 9x^2+25y^2+36x-200y+211=0 is Ellipse with (h,k)=(-2,4),a=5,b=3