1.

Let P be a point in first quadrant on parabola y^(2) = 2x whose focal distance is 5. If PF is perpendicular to SP (S is focus) which intersect x axis at point F, then the length of SF is :

Answer»

5

8

Solution :Let point P is `("at"^(2)," 2at")-=((t^(2))/(2),t)`
`because"FOCAL distance = 5"`
`THEREFORE""a+at^(2)=(1)/(2)(1+t^(2))=5`
`rArr""t=3` (in first quadrant)
`rArr"P is "((9)/(2), 3)`
`m_("SP")=(3-0)/((9)/(2)-(1)/(2))=(3)/(4)`

`tan theta=(3)/(4)`
From figure `cos theta=(5)/(SF)`
`(4)/(5)=(5)/(SF) rArr SF=(25)/(4)`


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