Home
Class 12
MATHS
Under rotation of axes through theta , x...

Under rotation of axes through `theta` , `x cosalpha + ysinalpha=P` changes to `Xcos beta + Y sin beta=P`, then

A

`cos beta = cos (alpha - theta)`

B

`cos alpha = cos (beta - theta)`

C

`sin beta = sin (alpha - theta)`

D

`sin alpha = sin (beta - theta)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`x cos alpha +y sin alpha +P`
Axis rotated through angle `theta`.
Transformed equation
`cos alpha (x cos theta - y sin theta) +sin alpha (x sin theta +y cos theta) = P`
`x cos (alpha -theta) +y sin (alpha -theta) = P rArr x cos beta +y sin beta = P` where,
`cos beta = cos (alpha-theta), sin beta = sin (alpha - theta)`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSTEM

    CENGAGE|Exercise Comprehension Type|4 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CENGAGE|Exercise Question Bank|22 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise JEE Main Previous Year|6 Videos

Similar Questions

Explore conceptually related problems

The lines x cos alpha+y sin alpha=P_(1) and x cos beta+y sin beta=P_(2) will be perpendicular,if :

If x cos alpha + y sin alpha = x cos beta + y sin beta = 2a then cos alpha cos beta =

The angle between the lines x cos alpha+y sin alpha=p_(1) and x cos beta+y sin beta=p_(2) when alpha>beta

If x=cos alpha+i sin alpha, y=cos beta+i sin beta then " (y)/(x)-(x)/(y)=

If x cos alpha + y sin alpha = x cos beta + y sin beta = a, 0

The angle between lines x cos alpha+y sin alpha=p_(1), and x cos beta+y sin beta=p_(2), where alpha>beta is

Prove that the area of the parallelogram formed by the lines x cos alpha+y sin alpha=p,x cos alpha+y sin alpha=q,x cos beta+y sin beta=r and x cos beta+y sin beta=sis+-(p-q)(r-s)csc(alpha-beta)