Home
Class 12
MATHS
Find the locus of the midpoints of the p...

Find the locus of the midpoints of the portion of the normal to the parabola `y^2=4a x` intercepted between the curve and the axis.

Text Solution

Verified by Experts

The correct Answer is:
`y^(2)=a(x-a)`
Normal at `P(at^(2),2at)" is "t=-tx+2at+at^(3)`.
It meets the axis y=0 at `G(2a+at^(2),0)`.
If (x,y) is the midpoint of PG, then
`2x=2a+at^(2)+at^(2),2y=2at`
Eliminating t, we have
`x-a=at^(2)-a((y)/(a))^(2)`
`or" "y^(2)=a(x-a)`
which is the required locus.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise 5.7|9 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Single)|98 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.5|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

Find the locus of the midpoints of the portion of the normal to the parabola y^(2)=4ax intercepted between the curve and the axis.

Find the locus of the mid points of the portion of the lines xsintheta+y costheta=p intercepted between the axes.

which Find the locus of the mid-point of the portion of the line x cos alpha+y sin alpha=p intercepted between the axes

Prove that the locus of the middle point of portion of a normal to y^(2) = 4ax intercepted between the curve & the axis is another parabola. Find the vertex & the latus rectum of the second parabola.

Find the locus of the mid-point of the portion of the line x cos alpha+y sin alpha=p which is intercepted between the axes.