Question

Find the coordinates of the vertex given the focus and directrix.

focus: (−10,−3)
directrix: y=−7

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Answer 1

The vertex of a parabola is equidistant from the focus and the directrix. The directrix is a horizontal line, so the vertex lies on the vertical line halfway between the focus and the directrix. Therefore, the x-coordinate of the vertex is -10, and the y-coordinate is the average of -3 and -7, which is -5.

So, the coordinates of the vertex are (-10, -5).