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  4. If the x-intercept of a focal chord of the parabola y2=8 x+4 y+4 is 3 , then the length of this chord is equal to

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Q. If the $x$-intercept of a focal chord of the parabola $y^2=8 x+4 y+4$ is 3 , then the length of this chord is equal to ___

JEE MainJEE Main 2023Conic Sections

Solution:

$ y^2=8 x+4 y+4$
$ (y-2)^2=8(x+1)$
$ y^2=4 a x$
$ a=2, X=x+1, Y=y-2$
focus $(1,2)$
$y -2= m ( x -1)$
Put $(3,0)$ in the above line $m =-1$
Length of focal chord $=16$