What is 25xx+9yy-18y-216=0 ?

The solution to 25xx+9yy-18y-216=0 is Ellipse with (h,k)=(0,1),a=3,b=5

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25xx+9yy-18y-216=0

25 xx + 9 yy - 18 y - 216 = 0

(h, k) = (0, 1), a = 3, b = 5

Solution steps

25 xx + 9 yy - 18 y - 216 = 0

Rewrite

25 xx + 9 yy - 18 y - 216 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 1 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 1), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 5, a = 3

2 x^{2} + 5 y^{2} = 14

5 x^{2} + y^{2} + x + 8 y + 5 = 0

\frac{( x - 5 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{36} = 1

\frac{( x - 0 ) ^{2}}{36} + \frac{( y - 0 ) ^{2}}{20} = 1

49 x^{2} + 4 y^{2} - 196 = 0

What is 25xx+9yy-18y-216=0 ?
The solution to 25xx+9yy-18y-216=0 is Ellipse with (h,k)=(0,1),a=3,b=5