JEE MAIN - Mathematics (2023 - 1st February Evening Shift - No. 17)
If the $$x$$-intercept of a focal chord of the parabola $$y^{2}=8x+4y+4$$ is 3, then the length of this chord is equal to ____________.
Answer
16
Explanation
$$
\begin{aligned}
& y^2=8 x+4 y+4 \\\\
& (y-2)^2=8(x+1) \\\\
& Y^2=4 a X \\\\
& a=2, X=x+1, Y=y-2 \\\\
& \text { focus }(1,2) \\\\
& y-2=m(x-1)
\end{aligned}
$$
Put $(3,0)$ in the above line $\mathrm{m}=-1$
Length of focal chord $=16$
Put $(3,0)$ in the above line $\mathrm{m}=-1$
Length of focal chord $=16$
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