Home
Class 12
MATHS
Two rods are rotating about two fixed po...

Two rods are rotating about two fixed points in opposite directions. If they start from their position of coincidence and one rotates at the rate double that of the other, then find the locus of point of the intersection of the two rods.

Text Solution

Verified by Experts

Let PB make angle `theta` and PA make angle `2theta` with x-axis.
Let P be (h,k).
`tantheta=(k)/(h_a)` (1)
`tan2theta=(k)/(h-a)` (2)
From (2), we get
`(2tantheta)/(1-tan^2theta)=(k)/(h-a)`

Putting value of `tantheta` from (1),we get
`(2((k)/(h+a)))/(1-((k)/(h+a))^2)=(k)/(h-a)`
`rArrh^2k^2-2ah-3a^2=0`
`rArrx^2+y62-2ax-2a^2=0`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.1|6 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.2|8 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

Find the number of point of intersection of two straight lines .

Two lines are drawn at right angles, one being a tangent to y^2=4a x and the other x^2=4b ydot Then find the locus of their point of intersection.

Find the area bounded by the curves y=s in xa n dy=cosx between two consecutive points of the intersection.

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.

Two wave pulses travel in opposite directions on a string and approach each other. The shape of the one pulse is inverted with respect to the other. What does that mean?

If a point A(6,8) rotates through an angle 90^o about the origin in the anticlockwise direction ,find the new position of A.

In a children's park a heavy rod is pivoted at the centre and is made to rotate about the pivot so that the rod always remains horizontal. Two kids hold the rod near the ends and thus rotate with the rod figure. Let the mas of each kid be 15 kg, the distance between the points of the rod where the two kids hold it be 3.0 m and suppose that the rod rotates at the rate of 20 revolutions per minute. Find the force of friction exerted by the rod on one of the kids.