What is 16x^2+25y^2-128x+100y=0 ?

The solution to 16x^2+25y^2-128x+100y=0 is Ellipse with (h,k)=(4,-2),a=(sqrt(89))/2 ,b=(2sqrt(89))/5

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16x^2+25y^2-128x+100y=0

16 x^{2} + 25 y^{2} - 128 x + 100 y = 0

(h, k) = (4, - 2), a = \frac{89}{2}, b = \frac{2 89}{5}

Solution steps

16 x^{2} + 25 y^{2} - 128 x + 100 y = 0

Rewrite

16 x^{2} + 25 y^{2} - 128 x + 100 y = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( \frac{89}{2} ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( \frac{2 89}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 2), a = \frac{89}{2}, b = \frac{2 89}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), a = \frac{89}{2}, b = \frac{2 89}{5}

\frac{( ( x + 0 ) ^{2} )}{40} + \frac{( ( y + 0 ) ^{2} )}{32} = 1

\frac{( x - 5 ) ^{2}}{16} + \frac{( y + 15 ) ^{2}}{25} = 1

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

\frac{x ^{2}}{3. 5 ^{2}} + \frac{y ^{2}}{2. 5 ^{2}} = 1

12 x^{2} + y^{2} = 24

What is 16x^2+25y^2-128x+100y=0 ?
The solution to 16x^2+25y^2-128x+100y=0 is Ellipse with (h,k)=(4,-2),a=(sqrt(89))/2 ,b=(2sqrt(89))/5