Question

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

Solution

Correct option is

A square

Let the two perpendicular lines be taken as the coordinate axes. If (h, k) be any point on the locus, then according to the given condition | h | + | k| = 1  

⇒ locus of (hk) is | x | + | y | = 1  

This consists of four line segments which enclose a square as shown in fig.

                                                                        

SIMILAR QUESTIONS

Q1

If abc form a G.P. with common ratio r, the sum of the ordinates of the points of intersection of the line ax + by + c = 0 and the curve x + 2y2= 0 is

Q2

Orthocenter of the triangle with vertices (0,0), (3, 4) and (4, 0) is

Q3

The number of integral points (integral point means both the coordinates should be integer) that lie exactly in the interior of the triangle with vertices (0, 0), (0, 21), and (21, 0) is

Q4

Let P = (–1, 0), Q = (0, 0) and  be three points. Then the equation of the bisector of the angle PQR is 

Q5

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.

Q6

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 

Q7

 

The diagonals of a parallelogram PQRS are long the lines

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

Q8

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

Q9

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

Q10

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.