Question

The locus of the points of trisection of the double ordinates of a parabola is a

• A. pair of lines
• B. circle
• C. parabola
• D. straight line

Answer 1

The correct option is C parabola

Let the coordinate of an end point of a double ordinate be $P(a{t}^2,2at)$
then the coordinate of other end are $Q(a{t}^2,-2at)$
The coordinate of the point M of trisection are $(a{t}^2,\frac{-2at}{3})$ or $(a{t}^2,\frac{2at}{3})$
So the locus of M in either case is $9y^2=4ax$, which is a parabola