SOLUTION: Write an equation for the set of all points in the plane equidistant from (-4.-13/2) and x=4.
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Question 1138876: Write an equation for the set of all points in the plane equidistant from (-4.-13/2) and x=4.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The set of points equidistant from a fixed point (focus) and fixed line (directrix) is a parabola.
With a vertical directrix at x=4 and a focus at (-4,-6.5), the parabola opens to the left.
The vertex is the point on the axis of symmetry equidistant from the focus and directrix, so the vertex is (0,-6.5).
The equation of a parabola opening left or right with vertex at (0,-6.5) is
In the equation in that form, p is the directed distance from the vertex to the focus. With the vertex at x=0 and the focus at x=-4, p = -4.
So 4p = -16, and the completed equation is
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