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

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

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

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

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

Solution steps

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

Rewrite

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

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

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{9} = 1

5 x^{2} + 9 y^{2} = 45

9 x^{2} + y^{2} = 81

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

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 4 ) ^{2}}{9} = 1

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