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Grade 11Analytical Geometry

Length of the chord As in the preceding article,

 

Length of the chord

As in the preceding article, the abscissae of the points common to the straight line y = mx + c and the parabola y2 = 4ax are given by the equation m2x2 + (2mx – 4a) x + c2 = 0. 

={[4(mc-2a)^2]/m^4}-{(4c^2)/m^2}...........HOW????

Profile image of PRATIK
8 Years agoGrade 11
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1 Answer

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Vijaya

8 Years ago
To obtain the points common to the straight line y = mx + c and the parabola y2= 4ax :
  1. Substitue y= mx + c in the given equation of parabola y2= 4ax.
  2. Doing that we get (mx +c)2= 4ax.
    > m2x2 + c2 + 2mxc = 4ax 
    > m2x2 + c2 + 2mxc -4ax =0
    > m2x2 + 2x (mc- 4a) + c2 = 0
     the above equation is quadratic equation in x
     to obtain the abcissae of the points in common to the straight line y= mx+c and the parabola y2 = 4ax use the quadratic             roots formula  
     dividing  the above equation with m2
    > x2+ 2x(mc – 2a)/m2 + c2/ m2 = 0 …...(1)
    calculate the discriminant for the above eqaution 
    D= [2(mc – 2a)/ m2]2 – 4(c2 / m2)
       = {4(mc – 2a)2 /m4 } – {4(c2/ m2)}
 

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