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QJEEM23Ma6a52: JEE Main 2023 Mathematics - Class 11 JEEM23Ma6a52 Solution: If the -intercept of a focal chord of the parabola is 3, then…

If the xx -intercept of a focal chord of the parabola y2=8x+4y+4y^{2}=8x+4y+4 is 3, then the length of this chord is equal to ____________.

Step-by-Step Verified Solution

amp;y2=8x+4y+4amp;(y−2)2=8(x+1)amp;Y2=4aXamp;a=2,X=x+1,Y=y−2amp; focus (1,2)amp;y−2=m(x−1)\begin{aligned}& 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 \\\\& \text { focus }(1,2) \\\\& y-2=m(x-1)\end{aligned}

Put (3,0)(3,0) in the above line m=−1\mathrm{m}=-1

Length of focal chord =16=16

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