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Question

If the focus of a parabola is (2,1) and equation of the directrix is x+y=3, find the vertex of the parabola.

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Solution

x+y=3m=1
(2,1)m=1
y1=1(x+2)
y1=x+2
xy+3=0
xy+3=0
x+y3=0
2x=0
x=0;y=3
Vertex=
Midpoint of focus and directrix
=022,3+12=(1,2)

1126293_1038999_ans_8c891a67e6a54da8b4fdc8a7f0063508.png

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