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M is the foot of the perpendicular from ...

`M` is the foot of the perpendicular from a point `P` on a parabola `y^2=4a x` to its directrix and `S P M` is an equilateral triangle, where S is the focus. Then find `S P` .

Text Solution

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From the definition of the parabola, we have SP = PM
Now, triangle SP M is equilateral.
Therefore, SP=PM=SM.
From the figure, in triangle SLM,
`SM=Sl" cosec "30^(@)=2axx2=4a`
`:." "SP=4a`
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