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

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)