What is the focus of (2x+3y^2=0)

Question

What is the focus for the comic equation 2x+3y^2=0

Answer 1

2x+3y²=0, 

⅔x+y²=0, -⅔x=y² has its vertex at (0,0). The x-axis is the axis of symmetry. The focus and vertex lie on this axis, so the y-coordinate of both is zero. The focal distance satisfies the equation 4f=-⅔, f=-⅙. The focus is measured from the position of the vertex so the focus is at (-⅙,0).