What is 9y^2+90y+4x^2-16x+205=0 ?

The solution to 9y^2+90y+4x^2-16x+205=0 is Ellipse with (h,k)=(2,-5),a=3,b=2

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9y^2+90y+4x^2-16x+205=0

9 y^{2} + 90 y + 4 x^{2} - 16 x + 205 = 0

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

Solution steps

9 y^{2} + 90 y + 4 x^{2} - 16 x + 205 = 0

Rewrite

9 y^{2} + 90 y + 4 x^{2} - 16 x + 205 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

49 x^{2} + 81 y^{2} = 3969

16 x^{2} - 32 x + 7 y^{2} - 33 - 42 y = 0

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 2 ) ^{2}}{8} = 1

11 x^{2} + 2 y^{2} - 22 = 0

\frac{( y + 3 ) ^{2}}{81} + \frac{( x - 7 ) ^{2}}{64} = 1

What is 9y^2+90y+4x^2-16x+205=0 ?
The solution to 9y^2+90y+4x^2-16x+205=0 is Ellipse with (h,k)=(2,-5),a=3,b=2