What is 28x^2+64y^2-28x+128y-377=0 ?

The solution to 28x^2+64y^2-28x+128y-377=0 is Ellipse with (h,k)=(1/2 ,-1),a=4,b=sqrt(7)

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28x^2+64y^2-28x+128y-377=0

28 x^{2} + 64 y^{2} - 28 x + 128 y - 377 = 0

(h, k) = (\frac{1}{2}, - 1), a = 4, b = 7

Solution steps

28 x^{2} + 64 y^{2} - 28 x + 128 y - 377 = 0

Rewrite

28 x^{2} + 64 y^{2} - 28 x + 128 y - 377 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{1}{2} ) ^{2}}{4 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, - 1), a = 4, b = 7

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, - 1), a = 4, b = 7

64 x^{2} + 25 y^{2} = 1600

9 x^{2} - 18 x + 4 y^{2} + 16 y = 11

16 x^{2} + 64 y^{2} = 128

x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

x^{2} + 4 y^{2} = 12

What is 28x^2+64y^2-28x+128y-377=0 ?
The solution to 28x^2+64y^2-28x+128y-377=0 is Ellipse with (h,k)=(1/2 ,-1),a=4,b=sqrt(7)