JEE Advanced 2015 Paper 1Question 1
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
Parabola
Answer$4$
Solution
Reflection in $x+y+4=0$ sends $(x,y)\to(-y-4,-x-4)$. Curve $C$: $(X+4)^2=-4(Y+4)$. At $Y=-5$: $(X+4)^2=4$, $X=-2,-6$. $AB=4$.