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SVEN [57.7K]
3 years ago
10

Find an equation of the parabola with vertex , − 5 − 5 and directrix = x − 12 .

Mathematics
1 answer:
olchik [2.2K]3 years ago
7 0

Answer:


   x=−y26+y3−136


Explanation:


Given -


Vertex (−2,1)

Directrix x=1


The vertex is in the 2nd quadrant. The directrix is parallel to the y-axis. So, the parabola opens to the left. The vertex of the parabola is not the origin. Then its general form is -


   (y−k)2=−4.a.(x−h)


Where -

h and k are the coordinates of the vertex.


   h=−2)


   k=1


   a=1.5 half the distance between Directrix and vertex [= distance between focus and vertex]

Substitute these values in the equation


   (y−1)2=−4.1.5.(x+2)

   y2−2y+1=−6x−12

   −6x−12=y2−2y+1

   −6x=y2−2y+1+12

   x=y2−6−2y−6+13−6


   x=−y26+y3−136

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Q -------------R------------S

suppose this is your line,

R is the mid point

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QR = 2x
and
RS = x+3

as R is the mid point of QS
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