Find the coordinates of the missing endpoint if M is the midpoint of DF F(2,9) M(-1,6)
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Answer:
Step-by-step explanation:
We want to find the equation of the parabola with a focus of and directrix
.
Considering the directrix, the quadratic graph must open downwards.
The equation of this parabola is given by the formula,
, where
is the vertex of the parabola.
The axis of this parabola meets the directrix at .
Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,
and
.
The equation of the parabola now becomes,
.
Also is the distance between the vertex and the directrix.
This implies that .
Since the parabola turns downwards,
.
Our equation now becomes,
.
.
We make y the subject to get,
.
This is the same as
.
