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vishal singh Grade: 11
        

how to find the equation of directrix if vertex is(1,-1)&focus is(2,3)

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

vertex(1,-1) , focus(2,3)       (given)


let directrix cuts the axis of parabola at (h,k) then


vertex is midpoint of line joining focus & point at which directrix cuts the axis of parabola...


from above statement , (h+2)/2 = 1        &   (k+3)/2 = -1


                                      (h,k) = (0,-5)


slope of directrix is m & slope of axis is m1 then


mm1 = -1


m1 = 4/1 = 4


m = -1/4


now eq of directrix : (y+5) = (x-0)(-1/4)


                           x+4y+20 = 0              .................1


since eccentricity of parabola is 1 so


  SP = ePM


distance of any point from directrix = e (distance of any point on parabola from focus)


x+4y+20/(17)1/2 = [(x-2)2+(y-3)2]1/2 


this is the required eq


approve if u like my ans


 

6 years ago
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