What is 25x^{(2)}+16y^{(2)}-96y-156=0 ?

The solution to 25x^{(2)}+16y^{(2)}-96y-156=0 is Ellipse with (h,k)=(0,3),a=2sqrt(3),b=(5sqrt(3))/2

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25x^{(2)}+16y^{(2)}-96y-156=0

25 x^{(2)} + 16 y^{(2)} - 96 y - 156 = 0

(h, k) = (0, 3), a = 23, b = \frac{5 3}{2}

Solution steps

25 x^{2} + 16 y^{2} - 96 y - 156 = 0

Rewrite

25 x^{2} + 16 y^{2} - 96 y - 156 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 3), a = 23, b = \frac{5 3}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 3), b = \frac{5 3}{2}, a = 23

\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{16} = 1

5 x^{2} + 20 y^{2} - 25 x - 10 y = 5

2 x^{2} + 5 y^{2} + 8 x - 10 y - 27 = 0

\frac{( x - 4 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{20} = 1

\frac{x ^{2}}{13} + \frac{y ^{2}}{9} = 1

What is 25x^{(2)}+16y^{(2)}-96y-156=0 ?
The solution to 25x^{(2)}+16y^{(2)}-96y-156=0 is Ellipse with (h,k)=(0,3),a=2sqrt(3),b=(5sqrt(3))/2