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  4. Aray of light travelling along a line parallel to axis of parabola and moves along parallel to directrix after reflection from (1,2) on surface of parabola. If focus of parabola is (2,2+√3), then length of latus rectum will be

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Q. Aray of light travelling along a line parallel to axis of parabola and moves along parallel to directrix after reflection from $(1,2)$ on surface of parabola. If focus of parabola is $(2,2+\sqrt{3})$, then length of latus rectum will be

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Solution:

$\because$ Light rays after reflection passes through focus and reflected ray is parallel to directrix.
$\therefore$ point $(1,2)$ will be one extremity of LR.
$\therefore$ Length of $L R=2 \sqrt{(2-1)^{2}+(2+\sqrt{3}-2)^{2}}=4 $