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The mirror image of the focus to the par...

The mirror image of the focus to the parabola `4(x + y) = y^(2)` w.r.t. the directrix is

A

(0, 2)

B

(2, 2)

C

(-4, 2)

D

(-2, 2)

Text Solution

Verified by Experts

The correct Answer is:
C
Given parabola is `y^(2) = 4x + 4y`
`implies y^(2) - 4y = 4x " "implies y^(2) - 4y + 4 = 4x +4 `
` implies (y-2)^(2) = 4(x+1)`
` implies Y^(2) =4x, " "X = x+1`
`Y=y-2`
`:.` Focus : (a,0)
` X =a =1 " "Y=0`

` implies ` Focus : (a,0)
`X =a = 1 " " Y=0`
`implies x +1 = 1 implies y-2=0`
` implies x =0 implies y=2`
F :(0,2)
Directrix : X = -a
`implies x +1 =-1 " "implies x +2 =0`
` :. (alpha + 0)/(2) = -2 " "implies alpha = -4`
Image of (0,2) = (-4,2)
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