What is 16x^2+25y^2-64x+150y-111=0 ?

The solution to 16x^2+25y^2-64x+150y-111=0 is Ellipse with (h,k)=(2,-3),a=5,b=4

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16x^2+25y^2-64x+150y-111=0

16 x^{2} + 25 y^{2} - 64 x + 150 y - 111 = 0

(h, k) = (2, - 3), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} - 64 x + 150 y - 111 = 0

Rewrite

16 x^{2} + 25 y^{2} - 64 x + 150 y - 111 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 3), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), a = 5, b = 4

25 x^{2} + 9 y^{2} - 225 = 0

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

x^{2} + 4 y^{2} - 6 x + 5 = 0

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{9} = 1

x^{2} + 9 y^{2} = 36

What is 16x^2+25y^2-64x+150y-111=0 ?
The solution to 16x^2+25y^2-64x+150y-111=0 is Ellipse with (h,k)=(2,-3),a=5,b=4