What is 16x^2+25y^2+64x-200y+64=0 ?

The solution to 16x^2+25y^2+64x-200y+64=0 is Ellipse with (h,k)=(-2,4),a=5,b=4

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16x^2+25y^2+64x-200y+64=0

16 x^{2} + 25 y^{2} + 64 x - 200 y + 64 = 0

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

Solution steps

16 x^{2} + 25 y^{2} + 64 x - 200 y + 64 = 0

Rewrite

16 x^{2} + 25 y^{2} + 64 x - 200 y + 64 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

5 x^{2} + 10 y^{2} + 125 x + 125 y + 44 = 0

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{9} = 1

\frac{( x - 7 ) ^{2}}{25} + \frac{( y + 9 ) ^{2}}{36} = 1

\frac{x ^{2}}{2. 6 ^{2}} + \frac{y ^{2}}{2.4 3 ^{2}} = 1

What is 16x^2+25y^2+64x-200y+64=0 ?
The solution to 16x^2+25y^2+64x-200y+64=0 is Ellipse with (h,k)=(-2,4),a=5,b=4