What is 64x^2-192x-156+100y^2-200y=0 ?

The solution to 64x^2-192x-156+100y^2-200y=0 is Ellipse with (h,k)=(3/2 ,1),a= 5/2 ,b=2

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64x^2-192x-156+100y^2-200y=0

64 x^{2} - 192 x - 156 + 100 y^{2} - 200 y = 0

(h, k) = (\frac{3}{2}, 1), a = \frac{5}{2}, b = 2

Solution steps

64 x^{2} - 192 x - 156 + 100 y^{2} - 200 y = 0

Rewrite

64 x^{2} - 192 x - 156 + 100 y^{2} - 200 y = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{3}{2}, 1), a = \frac{5}{2}, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{2}, 1), a = \frac{5}{2}, b = 2

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{81} = 1

49 x^{2} + 4 y^{2} + 98 x - 147 = 0

9 x^{2} + 25 y^{2} - 144 x + 200 y + 751 = 0

\frac{4 x ^{2}}{19} + \frac{2 y ^{2}}{19} = 1

2 x - x^{2} - 4 y^{2} - 16 y - 1 = 0

What is 64x^2-192x-156+100y^2-200y=0 ?
The solution to 64x^2-192x-156+100y^2-200y=0 is Ellipse with (h,k)=(3/2 ,1),a= 5/2 ,b=2