What is 8x^2+16x+2y^2=0 ?

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

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8x^2+16x+2y^2=0

8 x^{2} + 16 x + 2 y^{2} = 0

(h, k) = (- 1, 0), a = 1, b = 2

Solution steps

8 x^{2} + 16 x + 2 y^{2} = 0

Rewrite

8 x^{2} + 16 x + 2 y^{2} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 1, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), b = 2, a = 1

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

\frac{( x - 3 ) ^{2}}{100} + \frac{( y + 4 ) ^{2}}{64} = 1

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

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

2 x^{2} + 3 y^{2} = 12

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