Find an equation of the parabola described and state the two points that define the latus rectum. -Focus at (0, 1); directrix the line y = -1 A) x² = 4y; latus rectum: (2, 1) and (-2, 1) B) x² = 8y; latus rectum: (4, 1) and (-4, 1) C) x² = 4y; latus rectum: (1, 2) and (-1, 2) D) y² = 8x; latus rectum: (3, 4) and (-3, 4)

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Quizplus · Accepted Answer

The focus of the parabola is at (0, 1) and the directrix is the line y = -1. The distance between the focus and the directrix is 2, which means the value of 4p (where p is the distance from the vertex to the focus) is 4*1 = 4. Since the focus and directrix are vertically aligned, the parabola opens upwards, and its equation is of the form x^2 = 4py, which simplifies to x^2 = 4y. The latus rectum is the line segment through the focus parallel to the directrix and has endpoints that lie on the parabola. Its length is 4p = 4, and since the focus is at (0, 1), the endpoints of the latus rectum are at (2, 1) and (-2, 1), because it is 2 units to the left and right of the focus along the line y = 1.

Find an Equation of the Parabola Described and State the Two