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

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

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

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

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

Solution steps

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

Rewrite

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

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

16 y^{2} + 25 x^{2} - 80 x + 36 y + 80 = 0

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

9 x^{2} + 4 y^{2} - 72 x - 24 y + 144 = 0

4 x^{2} + 25 y^{2} - 8 x + 100 y + 4 = 0

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