What is x^2+2y^2+2x-20y=-43 ?

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

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x^2+2y^2+2x-20y=-43

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

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

Solution steps

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

Rewrite

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

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

16 x^{2} + 16 y^{2} = 4 y^{2} + 20 y + 25

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

4 x^{2} + 8 y^{2} - 8 x + 48 y + 44 = 0

\frac{( ( x - 5 ) ^{2} )}{9} + \frac{( ( y - 4 ) ^{2} )}{36} = 1

15 x^{2} + 10 y^{2} = 150

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