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

x^{2} + 2 z^{2} + 10 x - 16 z + 1 = 0

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

9 x^{2} + 4 y^{2} - 18 x + 24 y = 36

9 > x^{2} + 9 y^{2}

27 x^{2} + 6 y^{2} - 5 = 0

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