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JEE Advanced 2015Paper 1
Exam
JEE Advanced
Year
2015
Paper
Paper 1
Subject
Mathematics
Chapter
Straight Lines

JEE Advanced 2015 · Paper 1 · Mathematics · Straight Lines

Let the curve C be the mirror image of the parabola y ^ 2 = 4x with...

Let the curve C be the mirror image of the parabola y2{y}^{2}=4x= 4x with respect to the line x+y+4=0.x + y + 4 = 0 . If A and B are the points of intersection of C with the line y=−5,y = - 5, then the distance between A and B is

Let the curve C be the mirror image of the parabola y ^ 2 = 4x with respect to the line x + y + 4 = 0 . If A and B are

Correct answer

4

Step-by-step solution

Let the curve C be the mirror image of the parabola y ^ 2 = 4x with respect to the line x + y + 4 = 0 . If A and B are
Equation of AA′{\text{AA}}^{′} is
y+5=1(x−α)y + 5 = 1\left(x - \alpha\right)
⇒y=x−α−5⇒ y = x - \alpha - 5
y−x=−α−5y - x = - \alpha - 5 ...(i)
Also
x+y=−4x + y = - 4
y=−α−92y = \dfrac{- \alpha - 9}{2}
2x=α+12x = \alpha + 1
⇒x=α+12⇒ x = \dfrac{\alpha + 1}{2}
M≡(α+12,−α−92)M ≡ \left(\dfrac{\alpha + 1}{2}, \dfrac{- \alpha - 9}{2}\right)
A′=(1,α−4){A}^{′} = \left(1, \alpha - 4\right)
A′{A}^{′} lies on parabola
Now,
α2+16+8α=4{\alpha}^{2} + 16 + 8\alpha = 4
⇒α2+8α+12=0⇒ {\alpha}^{2} + 8\alpha + 12 = 0
⇒α=−2,−6⇒ \alpha = - 2, - 6
AB = distance = 4 units
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