What is (y+2)^2=1-2(x+1)^2 ?

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

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(y+2)^2=1-2(x+1)^2

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

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

Solution steps

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

Rewrite

(y + 2)^{2} - 1 + 2 (x + 1)^{2} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

4 (x - 3)^{2} + 2 y^{2} = 8

9 x^{2} + 36 y^{2} + 18 x - 360 y + 585 = 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{24} = 1

x^{(2)} + 4 y^{(2)} - 6 x + 16 y + 21 = 0

16 x^{2} + 25 y^{2} - 64 x - 336 = 0

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