What is 16x^2+y^2-64x+8y+16=0 ?

The solution to 16x^2+y^2-64x+8y+16=0 is Ellipse with (h,k)=(2,-4),a=2,b=8

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16x^2+y^2-64x+8y+16=0

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

(h, k) = (2, - 4), a = 2, b = 8

Solution steps

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

Rewrite

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 4), a = 2, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 4), b = 8, a = 2

\frac{1}{2} x^{2} + 6 y^{2} - 5 x + \frac{1}{4} y + 8 = 0

x^{2} + \frac{y ^{2}}{36} = 1

α^{2} + 2 β^{2} = 1

8 (x + \frac{6}{7})^{2} + 3 (y - \frac{3}{2})^{2} = 27

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

What is 16x^2+y^2-64x+8y+16=0 ?
The solution to 16x^2+y^2-64x+8y+16=0 is Ellipse with (h,k)=(2,-4),a=2,b=8