Home
Class 12
MATHS
If length of focal chord P Q is l , and ...

If length of focal chord `P Q` is `l ,` and `p` is the perpendicular distance of `P Q` from the vertex of the parabola, then prove that `lprop1/(p^2)dot`

Text Solution

Verified by Experts


From the figure, `PQ=4a" cosec"^(2)theta=l` (given)
Also, in triangle OMS, `sintheta=(p)/(a)`
`:." "l=4a(a^(2))/(p^(2))prop(1)/(p^(2))`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.4|13 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.5|9 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.2|17 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE ENGLISH|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

Prove that the length of a focal chord of a parabola varies inversely as the square of its distance from the vertex.

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

if p: q :: r , prove that p : r = p^(2): q^(2) .

Find the electric field at a point P on the perpendicular bisector of a uniformly charged rod. The length of the rod is L, the charge on it is Q and the distance of P from the centre of the rod is a.

Consider the parabola y^(2)=8x, if the normal at a point P on the parabola meets it again at a point Q, then the least distance of Q from the tangent at the vertex of the parabola is

Consider the parabola y^(2)=8x, if the normal at a point P on the parabola meets it again at a point Q, then the least distance of Q from the tangent at the vertex of the parabola is

Find the electric field at a point P on the perpendicular bisector of a uniformly charged rod. The lengthof the rod is L, the charge on it is Q and the distance of P from the centre of the rod is a.

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

Prove that q^^~p -=~ (q to p)

The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with abscissa 1. Then the value of pa n dq for which the distance between the vertex of the parabola and the x-axis is the minimum is (a) p=-1,q=-1 (b) p=-2,q=0 (c) p=0,q=-2 (d) p=3/2,q=-1/2