What is x^2+25y^2-200y+375=0 ?

The solution to x^2+25y^2-200y+375=0 is Ellipse with (h,k)=(0,4),a=5,b=1

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x^2+25y^2-200y+375=0

x^{2} + 25 y^{2} - 200 y + 375 = 0

(h, k) = (0, 4), a = 5, b = 1

Solution steps

x^{2} + 25 y^{2} - 200 y + 375 = 0

Rewrite

x^{2} + 25 y^{2} - 200 y + 375 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 4 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 4), a = 5, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 4), a = 5, b = 1

\frac{( x + 1 ) ^{2}}{36} + \frac{( y + 3 ) ^{2}}{25} = 1

x^{2} + 9 y^{2} + 2 x - 18 y + 1 = 0

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

\frac{x ^{2}}{16} + \frac{y ^{2}}{80} = 1

4 x^{2} + y^{2} - 16 x + 2 y + 1 = 0

What is x^2+25y^2-200y+375=0 ?
The solution to x^2+25y^2-200y+375=0 is Ellipse with (h,k)=(0,4),a=5,b=1