What is 36x^2+25y^2-50y-875=0 ?

The solution to 36x^2+25y^2-50y-875=0 is Ellipse with (h,k)=(0,1),a=5,b=6

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36x^2+25y^2-50y-875=0

36 x^{2} + 25 y^{2} - 50 y - 875 = 0

(h, k) = (0, 1), a = 5, b = 6

Solution steps

36 x^{2} + 25 y^{2} - 50 y - 875 = 0

Rewrite

36 x^{2} + 25 y^{2} - 50 y - 875 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 1 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 1), a = 5, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 6, a = 5

\frac{( x - 7 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{36} = 1

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

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{26}{16}} = 1

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

25 x^{2} + 9 y^{2} + 200 x - 36 y + 211 = 0

What is 36x^2+25y^2-50y-875=0 ?
The solution to 36x^2+25y^2-50y-875=0 is Ellipse with (h,k)=(0,1),a=5,b=6