What is 9x^2+25y^2+108x-200y+499=0 ?

The solution to 9x^2+25y^2+108x-200y+499=0 is Ellipse with (h,k)=(-6,4),a=5,b=3

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9x^2+25y^2+108x-200y+499=0

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

(h, k) = (- 6, 4), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

Rewrite

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{5 ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 4), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 4), a = 5, b = 3

25 x^{2} + 36 y^{2} + 100 x + 72 y - 764 = 0

\frac{2 x ^{2}}{25} + \frac{( y - 3 ) ^{2}}{49} = 1

2 x^{2} + y^{2} = 1

12 x^{2} + 4 y^{2} - 24 x - 4 y + 1 = 0

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{9} = 1

What is 9x^2+25y^2+108x-200y+499=0 ?
The solution to 9x^2+25y^2+108x-200y+499=0 is Ellipse with (h,k)=(-6,4),a=5,b=3