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if the axis of parabola y²=4x touches a circle of radius r such that the parabola cuts the circle at two distinct points at A and B and AB is the diameter of the circle then slope of AB is ?

if the axis of parabola y²=4x touches a circle of radius r such that the parabola cuts the circle at two distinct points at A and B and AB is the diameter of the circle then slope of AB is ?

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

general point on a parabola with eq y2 =4ax  is  (at2 ,2at)

but we have eq y2 =4x

 so a =1

   so genral point is (t2 ,2t) ..............1

parabola cuts the circle at two different points ,let these points be A,B..

A=(t12,2t1)  & B=(t22,2t2)

circle touches the x axis so the y coordinate of its center is +r when circle is drawn above x axis & -r when drawn below..

since AB is diameter then

    coordinate of center of circle=A+B/2=[(t12 +t22)/2 ,(t1+t2)]

  y coordinate of center =+ (r) or -(r)

            so t1+t2=+ (r) or -(r)         .................2

slope of AB=2(t2-t1)/(t22-t12)

                m=2/(t1+t2)

               m=2/r ,-2/r

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