What is 25x^2+4y^2-50x+16y-59=0 ?

The solution to 25x^2+4y^2-50x+16y-59=0 is Ellipse with (h,k)=(1,-2),a=2,b=5

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25x^2+4y^2-50x+16y-59=0

25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

(h, k) = (1, - 2), a = 2, b = 5

Solution steps

25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

Rewrite

25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 5, a = 2

5 x^{2} + 7 y^{2} = 35

(\frac{x ^{2}}{a}) + (\frac{y ^{2}}{b}) = 1

\frac{( x - 10 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

3 x^{2} + 2 y^{2} - 6 x + 4 y - 2 = 0

9 x^{(2)} + 25 y^{(2)} + 18 x + 150 y + 9 = 0

What is 25x^2+4y^2-50x+16y-59=0 ?
The solution to 25x^2+4y^2-50x+16y-59=0 is Ellipse with (h,k)=(1,-2),a=2,b=5