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

Suppose PQ is a double ordinate of the parabola $y^2=4ax$

Let R and S be the points of trisection of the double ordinates.

Let (h,k) be the coordinates of R.

Then,we have :

OL=h and RL=k

$\therefore RS=RL+LS=k+k=2k$

$\Rightarrow PR=RS=SQ=2k$ $\Rightarrow LP=LR+RP=k+2k=3k$

Thus,the coordinates of P are (h,3k) which lie on $y^2=4ax$

$\therefore 9k^2=4ah$

Hence,the locus of the point (h,k) is 9$y^2=4ax,i.e.y^2=\left(\frac{4a}{9}\right)$x,which represents a parabola.