- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

If all the lines given by the equation [itex](3\sin \theta + 5\cos \theta )x+(7\sin \theta - 3\cos \theta )y+11(\sin \theta - \cos \theta)=0 [/itex] pass through a fixed point (a,b) forall theta in R then |a-b|=

## Homework Equations

## The Attempt at a Solution

Dividing both sides by (3sin theta + 5cos theta)

[itex]x+ \dfrac{(7\sin \theta - 3\cos \theta)y+11(\sin \theta - \cos \theta)}{3\sin \theta + 5\cos \theta}=0[/itex]

This is of the form L1+λL2 and the fixed point is intersection of L1 and L2. Here x=0 and [itex]y=\dfrac{-11(\sin \theta - \cos \theta)}{(7\sin \theta - 3\cos \theta )}[/itex] However, the difference of the two depends on theta and is not constant. So how can it be fixed?