If PQ is a focal chord of the parabola y^2=4x | vedclass

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(B) The parabola is given by $y^2=4x$,which is of the form $y^2=4ax$ with $a=1$. The focus is $S(a,0) = (1,0)$.Since $PQ$ is a focal chord,the segment

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$\frac{5}{4}$

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(B) The parabola is given by $y^2=4x$,which is of the form $y^2=4ax$ with $a=1$. The focus is $S(a,0) = (1,0)$.Since $PQ$ is a focal chord,the segments $PS$ and $SQ$ are related to the semi-latus rectum $l=2a=2$ by the harmonic mean property: $\frac{1}{PS} + \frac{1}{SQ} = \frac{1}{a} = \frac{1}{1} = 1$.Given $P=(4,4)$ and $S=(1,0)$,the distance $PS = \sqrt{(4-1)^2 + (4-0)^2} = \sqrt{3^2 + 4^2} = \sqrt{9+16} = \sqrt{25} = 5$.Substituting $PS=5$ into the relation: $\frac{1}{5} + \frac{1}{SQ} = 1$.$\frac{1}{SQ} = 1 - \frac{1}{5} = \frac{4}{5}$.Therefore,$SQ = \frac{5}{4}$.

If $PQ$ is a focal chord of the parabola $y^2=4x$ with focus $S$ and $P=(4,4)$,then $SQ=$

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