What is 4x^2+25y^2-50y-75=0 ?

The solution to 4x^2+25y^2-50y-75=0 is Ellipse with (h,k)=(0,1),a=5,b=2

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4x^2+25y^2-50y-75=0

4 x^{2} + 25 y^{2} - 50 y - 75 = 0

(h, k) = (0, 1), a = 5, b = 2

Solution steps

4 x^{2} + 25 y^{2} - 50 y - 75 = 0

Rewrite

4 x^{2} + 25 y^{2} - 50 y - 75 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 1 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 1), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 1), a = 5, b = 2

x^{2} + 4 y^{2} - 2.71 = 0

\frac{( x - 5 ) ^{2}}{144} + \frac{( y + 2 ) ^{2}}{169} = 1

4 y^{(2)} + 2 x^{(2)} - 4 y - 8 x - 15 = 0

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

\frac{x ^{2}}{1} + \frac{y ^{2}}{a - 16} = 1

What is 4x^2+25y^2-50y-75=0 ?
The solution to 4x^2+25y^2-50y-75=0 is Ellipse with (h,k)=(0,1),a=5,b=2