JEE Advanced 2015 · Paper 1 · Mathematics Q42

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MathematicsInteger+4Question 42 of 60

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 the points of intersection of $C$ with the line $y=-5$ , then the distance between $A$ and $B$ is

Your answer

Answer and worked solution

Official answer: 4

Reflection. Reflecting in $x+y+4=0$ maps $(X,Y)\mapsto(-Y-4,-X-4)$ .

The curve C. $(X,Y)$ is on C when its image lies on $y^2=4x$ :
$(X+4)^2=-4(Y+4).$

Intersect with $Y=-5$ . $(X+4)^2=4$ , so $X=-2$ or $-6$ . Then $AB=4$ .

Answer: 4

Topics:Parabola Locus

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JEE Advanced 2015 · Paper 1, Mathematics question 42