Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.

Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping

show that the locus of the points of trisection of the double ordinates of a parabola forms a parabola

show that the locus of the  points of trisection of the double ordinates of  a parabola forms a parabola


1 Answers

25763 Points
3 years 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 = x
And n = (-y+2y)/3 = y/3 or y=3n
Now putting the values of m and n into the equation of the parabola, we get
(3n)2 = 4am or n2 = (4/9)am
And this is the equation of the parabola.
Arun (askIITians forum expert)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy


Get your questions answered by the expert for free