What is 4x^2+y^2-32x+4y+64=0 ?

The solution to 4x^2+y^2-32x+4y+64=0 is Ellipse with (h,k)=(4,-2),a=1,b=2

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4x^2+y^2-32x+4y+64=0

4 x^{2} + y^{2} - 32 x + 4 y + 64 = 0

(h, k) = (4, - 2), a = 1, b = 2

Solution steps

4 x^{2} + y^{2} - 32 x + 4 y + 64 = 0

Rewrite

4 x^{2} + y^{2} - 32 x + 4 y + 64 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 1, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), b = 2, a = 1

\frac{x ^{2}}{289} + \frac{y ^{2}}{225} = 1

2 x^{2} + 9 y^{2} - 18 = 0

4 x^{2} + y^{2} = 2 y + 3

9 y^{2} + z^{2} = 16

\frac{x ^{2}}{2.8 9 ^{2}} + \frac{y ^{2}}{2.8 4 ^{2}} = 1

What is 4x^2+y^2-32x+4y+64=0 ?
The solution to 4x^2+y^2-32x+4y+64=0 is Ellipse with (h,k)=(4,-2),a=1,b=2