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Question

The mirror image of the focus to the parabola 4(x+y)=y2 w.r.t. the directrix is

A
(0,2)
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B
(2,2)
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C
(4,2)
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D
(2,2)
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Solution

The correct option is D (2,2)
given, 4(x+y)=y2

4x=y24y

making perfect square in (y2)
y(x+1)=(y2)2.....(1)

comparing to y2=4ax
a=1

shifting origin to x=1 , y=2
(y)2=4(x)

focus is (0,2) so the image in x=1 i.e., directive is (2,2)

1367668_1177285_ans_1ab4ed0619c542168781ab7d8f39e60e.PNG

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