What is 16x^2+25y^2-64x-150y-11=0 ?

The solution to 16x^2+25y^2-64x-150y-11=0 is Ellipse with (h,k)=(2,3),a=(5sqrt(3))/2 ,b=2sqrt(3)

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16x^2+25y^2-64x-150y-11=0

16 x^{2} + 25 y^{2} - 64 x - 150 y - 11 = 0

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

Solution steps

16 x^{2} + 25 y^{2} - 64 x - 150 y - 11 = 0

Rewrite

16 x^{2} + 25 y^{2} - 64 x - 150 y - 11 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

36 (x^{2} - x) + 64 (y^{2} + 4 y) + 256 = 576

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{16} = 1

9 x^{2} + 25 y^{2} - 54 x - 100 y + 44 = 0

\frac{( x + 1 ) ^{2}}{8} + \frac{( y - \frac{3}{2} ) ^{2}}{4} = 1

\frac{x ^{2}}{1.5869} + \frac{y ^{2}}{0.9988} = 1

What is 16x^2+25y^2-64x-150y-11=0 ?
The solution to 16x^2+25y^2-64x-150y-11=0 is Ellipse with (h,k)=(2,3),a=(5sqrt(3))/2 ,b=2sqrt(3)