What is x^{(2)}+2y^{(2)}+2x-20y+43=0 ?

The solution to x^{(2)}+2y^{(2)}+2x-20y+43=0 is Ellipse with (h,k)=(-1,5),a=2sqrt(2),b=2

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x^{(2)}+2y^{(2)}+2x-20y+43=0

x^{(2)} + 2 y^{(2)} + 2 x - 20 y + 43 = 0

(h, k) = (- 1, 5), a = 22, b = 2

Solution steps

x^{2} + 2 y^{2} + 2 x - 20 y + 43 = 0

Rewrite

x^{2} + 2 y^{2} + 2 x - 20 y + 43 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 5), a = 22, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 5), a = 22, b = 2

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

\frac{x ^{2}}{27} + \frac{y ^{2}}{36} = 1

x^{2} + 4 y^{2} \leq 16

16 x^{2} + y^{2} - 32 x + 4 y - 44 = 0

x^{2} + 4 y^{2} - 36 = 0

What is x^{(2)}+2y^{(2)}+2x-20y+43=0 ?
The solution to x^{(2)}+2y^{(2)}+2x-20y+43=0 is Ellipse with (h,k)=(-1,5),a=2sqrt(2),b=2