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`        show that the locus of the  points of trisection of the double ordinates of  a parabola forms a parabola`
one year ago

```							Dear student Let y2 = 4ax be the parabola. Let AB be the Latus rectum.Let CD be an arbitrary double ordinate line parallel to the latus rectum (Points C and D are on the parabola) and let points M and N be the points of trisection i.e. they divide the double ordinate CD in 3 equal parts.Our objective is find the locus or path of these points M and N. Simply by observation, we can say that the path would be a parabola.We will now proceed to find the equation this parabola i.e. the locus of M and N.Let the co-ordinates of point C be (x, y). Pont D would be (x, -y).Let the co-ordinates of M be (m,n) and co-ordinates of point N be (m, -n)Now m = xAnd n = (-y+2y)/3 = y/3 or y=3nNow putting the values of m and n into the equation of the parabola, we get(3n)2 = 4am or n2 = (4/9)amAnd this is the equation of the parabola. RegardsArun (askIITians forum expert)
```
one year ago
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