A family of chords of the parabola is drawn so that their projections on a straight line inclined equally to both the axes are all of a constant length ; The locus of their middle point is the curve k where k =
1
2
3
Let the equation of straight line (h,k) as its mid point.
then .....................(1)
Any point on the line (1) is
Solving with the equation of parabola.
................(2)
which is quadratic in r.
The roots of the quadratic equation will be equal but of opposite sign as ( h, k) is the mid point
..............(3)
Length of the chord will be . Angle between the two lines will be and the projection of the chord on the given line will be
from (3) \& (4) we get
hence the locus of the middle point is
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