Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0,-2) A)y² = -8x B)x² = -8y C)x² = -2y D)y² = -2x E)x² = 2y

Question

Quizplus · Accepted Answer

Since the vertex is at the origin, the axis of symmetry is either the x-axis or the y-axis. Since the focus is (0,-2) and the vertex is at the origin, the axis of symmetry must be the x-axis. This means the parabola opens upwards. Therefore, the standard form of the equation of this parabola is x^2 = -4py where p is the distance from the vertex to the focus. In this case, p = 2. Substituting in gives x^2 = -8y, which is equivalent to the standard form given in choice B.

Find the Standard Form of the Equation of the Parabola