Home
Class 12
MATHS
If the length of focal chord of y^2=4a x...

If the length of focal chord of `y^2=4a x` is `l ,` then find the angle between the axis of the parabola and the focal chord.

Text Solution

Verified by Experts

The correct Answer is:
`pmsin^(-1)sqrt((4a)/(l))`
The length of focal chord inclined at angle `theta` with the positive x-axis is `4a" cosec"^(2)theta`.
Given the length of focal chord is l. Then,
`4a" coses"^(2)theta=l`
`:." "theta=pmsin^(-1)sqrt((4a)/(l))`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise 5.4|13 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.5|9 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.2|17 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

If the length of focal chord of y^(2)=4ax is l then find the angle between the axis of the parabola and the focal chord.

The length of a focal chord of the parabola y^(2)=4ax making an angle theta with the axis of the parabola is (a>0) is:

If the lsope of the focal chord of y^(2)=16x is 2, then the length of the chord, is

Let one end of focal chord of parabola y^2 = 8x is (1/2, -2) , then equation of tangent at other end of this focal chord is

If theta is the inclination of a focal chord of y^(2) = 4ax to its axis , then its length is

If the normal chord of the parabola y^(2)=4 x makes an angle 45^(@) with the axis of the parabola, then its length, is

If the point ( at^2,2at ) be the extremity of a focal chord of parabola y^2=4ax then show that the length of the focal chord is a(t+t/1)^2 .

One extremity of a focal chord of y^(2)=16x is A(1,4). Then the length of the focal chord at A is