Home
Class 11
MATHS
If the sum of the distances of a point f...

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is a (a) square (b)  a circle (c) a straight line         (d)  two intersecting lines

A

a square

B

a circle

C

a straight line

D

two intersecting lines

Text Solution

Verified by Experts

Let the two perpendicular lines be taken as the coordinates axes. If (h,k) is any point on the locus, then according to the given condition, |h|+|k|=1. Hence, the locus of (h,k) is |x|+|y|=1. This consists of four line segments enclosing a square as shown in the figure.
Promotional Banner

Similar Questions

Explore conceptually related problems

A rod of length l slides with its ends on two perpendicular lines. Find the locus of its midpoint.

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

If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight line c. a pair of straight line d. none of these

(2, 1) is the points of intersection of two lines

The locus of a point which moves such that the sum of the square of its distance from three vertices of a triangle is constant is a/an (a)circle (b) straight line (c) ellipse (d) none of these

An ellipse slides between two perpendicular straight lines. Then identify the locus of its center.

The distance of a point (x_1, y_1) from two straight lines which pass through the origin of coordinates is pdot Find the combined equation of these straight lines.

A line of fixed length a+b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of the point which divides this line into portions of length aa n db is a/an (a)ellipse (b) parabola (c)straight line (d) none of these

Let E_1a n dE_2, respectively, be two ellipses (x^2)/(a^2)+y^2=1,a n dx^2+(y^2)/(a^2)=1 (where a is a parameter). Then the locus of the points of intersection of the ellipses E_1a n dE_2 is a set of curves comprising (a)two straight lines (b) one straight line (c)one circle (d) one parabola