What is 4x^2+y^2-16x-2y+1=0 ?

The solution to 4x^2+y^2-16x-2y+1=0 is Ellipse with (h,k)=(2,1),a=2,b=4

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4x^2+y^2-16x-2y+1=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

5 x^{2} + z^{2} = 100

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

\frac{25 x ^{2}}{400 - 1 2 ^{2}} + \frac{16 y ^{2}}{400 - 1 2 ^{2}} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{225} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{25} = 1

What is 4x^2+y^2-16x-2y+1=0 ?
The solution to 4x^2+y^2-16x-2y+1=0 is Ellipse with (h,k)=(2,1),a=2,b=4