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

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

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

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

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

Solution steps

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

Rewrite

25 x^{2} + 50 x + 4 y^{2} - 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

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 2 ) ^{2}}{16} = 1

3 x^{2} + 8 y^{2} + 12 x + 48 y + 60 = 1

\frac{( x - 1 ) ^{2}}{4} + \frac{y ^{2}}{9} = 1

25 x^{(2)} + 16 y^{(2)} = 400

\frac{8 y}{1 + x ^{2} + y ^{2}} = 2

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