The equation of the latus rectum of a parabola is given by y=-3. The axis of the parabol is x=0 and vertex (0,0). Find the length of the focal chord that meets the parabola at (2,-1/3)   ans: 100/3

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aruv | High School Teacher | (Level 2) Valedictorian

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Latus rectum is focal chord which is perpendicular to the axis of the parabola.

Thus focus of the parabola =(0,-3)

Equation of directrix of parabola is  y=3

vertex (0,0)

Let P(x,y) be point on the parabola then by def of parabola


`` squaring both side and simplify


`x^2=-12y`                            (i)

equation of focal chord posses through (2,-1/3)



`y=-3-(8x)/6`                         (ii)

(i) and (ii) will intersect each other at point say Q







when  x=18 then



Thus coordinate of Q( 18,-27)

Thus distance between Q(18,-27) and (2,-1/3)



`d=(1/3)sqrt( 16^2xx3^2+80^2)=93.29/3`