What is 16x^2-64x+9y^2+9y+1=0 ?

The solution to 16x^2-64x+9y^2+9y+1=0 is Ellipse with (h,k)=(2,-1/2),a=(3sqrt(29))/8 ,b=(sqrt(29))/2

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16x^2-64x+9y^2+9y+1=0

16 x^{2} - 64 x + 9 y^{2} + 9 y + 1 = 0

(h, k) = (2, - \frac{1}{2}), a = \frac{3 29}{8}, b = \frac{29}{2}

Solution steps

16 x^{2} - 64 x + 9 y^{2} + 9 y + 1 = 0

Rewrite

16 x^{2} - 64 x + 9 y^{2} + 9 y + 1 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{3 29}{8} ) ^{2}} + \frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{29}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - \frac{1}{2}), a = \frac{3 29}{8}, b = \frac{29}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - \frac{1}{2}), b = \frac{29}{2}, a = \frac{3 29}{8}

\frac{( x + 5 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{144} = 1

\frac{8 x}{x ^{2} + y ^{2} + 1} = 1

(16 - x^{2} - 9 y^{2}) = - 1

36 x^{2} + 17 y^{2} - 648 x + 238 y + 689 = 0

25 x^{2} + 16 y^{2} - 200 x - 160 y + 400 = 0

What is 16x^2-64x+9y^2+9y+1=0 ?
The solution to 16x^2-64x+9y^2+9y+1=0 is Ellipse with (h,k)=(2,-1/2),a=(3sqrt(29))/8 ,b=(sqrt(29))/2