SOLUTION: HOW DO YOU GRAPH FOCUS AT (2,3) AND DIRECTRIX X= -1?

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Question 143561This question is from textbook
: HOW DO YOU GRAPH FOCUS AT (2,3) AND DIRECTRIX X= -1? This question is from textbook

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
HOW DO YOU GRAPH FOCUS AT (2,3) AND DIRECTRIX x+=+-1?

First plot the focus, indicated by "o" and the directrix
x+=+-1 which is a vertical line through -1 on the x-axis.
I'll draw it green:


Draw a perpendicular from the focus to the directrix

Then midpoint of that line segment is (1%2F2,3),
the vertex, so we will indicate it also with "o":

Draw a square ABOVE that line segment with it as one of
the sides:

Draw another square BELOW that line segment with it as one of
the sides:

Finally we sketch in the parabola passing through the vertex
an the upper right and lower corners of those squares,
respectively:

The equation of such a parabola is
%28y-k%29%5E2+=+4p%28x-h%29 where (h,k) is the vertex, and
4p is the length of the "latus rectum" or "focal chord".
The right sides of the two squares make up the "latus rectum"
or "focal chord". So its equation in standard form is
+%28y-3%29%5E2+=+6+%28x-1%2F2%29++
Edwin