To find the focus, directrix, and focal diameter of the parabola x = -2y^2, we need to first rewrite the equation in standard form (y = ax^2 + bx + c).
Given equation: x = -2y^2
Dividing by -2, we get: y^2 = -0.5x
Rearranging terms, we get: y^2 = (-1/2)x
Comparing this equation with standard form y^2 = 4ax, we see that a = -1/2.
The focus of the parabola is F(0, -1/(4a)) = F(0, 2). So, the focus of the parabola is (0, 2).
The directrix is at the distance a units from the vertex in the opposite direction to the y-axis. Therefore, the directrix is the line y = -2.
The focal diameter is the distance between two points on the parabola which lie on the line parallel to the directrix and pass through the focus. The coordinates of these points are (4a, 2) = (-1, 2) and (-1, 2), so the focal diameter is 2-(-2) = 4 units.
Therefore,
- Focus: F(0, 2)
- Directrix: y = -2
- Focal diameter: 4 units
Find the focus, directrix, and focal diameter of the parabola x=-2y^2
1 answer