What is 16x^2+16y^2=1+2x+x^2 ?

The solution to 16x^2+16y^2=1+2x+x^2 is Ellipse with (h,k)=(1/15 ,0),a= 4/15 ,b=sqrt(1/15)

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16x^2+16y^2=1+2x+x^2

16 x^{2} + 16 y^{2} = 1 + 2 x + x^{2}

(h, k) = (\frac{1}{15}, 0), a = \frac{4}{15}, b = \frac{1}{15}

Solution steps

16 x^{2} + 16 y^{2} = 1 + 2 x + x^{2}

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - \frac{1}{15} ) ^{2}}{( \frac{4}{15} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{15} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{15}, 0), a = \frac{4}{15}, b = \frac{1}{15}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{15}, 0), a = \frac{4}{15}, b = \frac{1}{15}

(\frac{x ^{2}}{9}) + (\frac{y ^{2}}{5}) = 1

9 x^{2} + 25 y^{2} + 36 x + 150 y + 36 = 0

16 x^{2} + 25 y^{2} - 224 x - 150 y + 1009 = 400

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

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

What is 16x^2+16y^2=1+2x+x^2 ?
The solution to 16x^2+16y^2=1+2x+x^2 is Ellipse with (h,k)=(1/15 ,0),a= 4/15 ,b=sqrt(1/15)