Question

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p andq are the intercepts of the line L on the new axes, then 

                                                          

Solution

Correct option is

0

Equation of the line L in the two coordinate system is

                                      

Where (X, Y) are the new coordinates of a point (xy) when the axes are rotated through a fixed angle, keeping the origin fixed. As the length of the perpendicular from the origin has not changed.

    

SIMILAR QUESTIONS

Q1

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio.

Q2

Let A0A1 2 A3 A4 A5 be a regular hexagon described in a circle of unit radius. Then the product of the length of the line segments A A1A0 A2and A0 A4 is 

Q3

 

The diagonals of a parallelogram PQRS are long the lines

x + 3y = 4 and 6x – 2y = 7, then PQRS must be a

Q4

The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is 

Q5

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

Q6

If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Q7

If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and (2a, –2a), then the orthocenter lies on the line.

Q8

If abc are unequal and different from 1 such that the points  are collinear, then  

Q9

If two vertices of a triangle are (–2, 3) and (5, –1), orthocentre lies at the origin and centroid on the line x + y = 7, then the third vertex lies at

Q10

If P is a point (xy) on the line, y = –3x such that P and the point (3, 4) are on the opposite sides of the line 3x – 4y = 8, then