What is 25x^2+9y^2+50x-108y+124=0 ?

The solution to 25x^2+9y^2+50x-108y+124=0 is Ellipse with (h,k)=(-1,6),a=3,b=5

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25x^2+9y^2+50x-108y+124=0

25 x^{2} + 9 y^{2} + 50 x - 108 y + 124 = 0

(h, k) = (- 1, 6), a = 3, b = 5

Solution steps

25 x^{2} + 9 y^{2} + 50 x - 108 y + 124 = 0

Rewrite

25 x^{2} + 9 y^{2} + 50 x - 108 y + 124 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 6), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 6), b = 5, a = 3

2 x^{2} + y^{2} - 2 x + 16 y + 1 = 0

x^{2} + y^{2} + 2 y \leq 0

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

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

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{12} = 1

What is 25x^2+9y^2+50x-108y+124=0 ?
The solution to 25x^2+9y^2+50x-108y+124=0 is Ellipse with (h,k)=(-1,6),a=3,b=5