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

The solution to x^2+4y^2-2x-16y=0 is Ellipse with (h,k)=(1,2),a=sqrt(17),b=(sqrt(17))/2

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

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

(h, k) = (1, 2), a = 17, b = \frac{17}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 17 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( \frac{17}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 2), a = 17, b = \frac{17}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 17, b = \frac{17}{2}

a - bi = \frac{1}{a + bi}

x^{2} + 4 y^{2} + 20 x + 44 y + 121 = 0

16 x^{2} + 7 y^{2} = 112

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

y^{2} = - 0.25 x^{2} + 1

What is x^2+4y^2-2x-16y=0 ?
The solution to x^2+4y^2-2x-16y=0 is Ellipse with (h,k)=(1,2),a=sqrt(17),b=(sqrt(17))/2