Determine the locus of a A boar moving so that it is equidis

Determine the locus of (a) A boar moving so that it is equidistant from the parallel banks of a stream (b) A swimmer maintaining the same distance from two floats (c) A police helicopter in pursuit of a car which has just passed the junction of two straight roads and which may be on either one of them (d) A treasure buried at the same distance from two intersecting straight roads Determine the locus of (a) a planet moving at a fixed distance from its sun; (b) a boat moving at a fixed distance from the coast of a circular island; (c) plants laid at a distance of 20 ft from a straight row of other plants;(d) the outer extremity of a clock had.

Solution

11.2

(a)

The locus of a boat moving so that it is equidistant from the parallel banks of a stream is a path exactly midway from both banks and parallel to both the banks.

-----------------------------------------------------------------------------------------------------------------------------------------------------------

(b)

The locus of a swimmer maintaining the same distance from two floats is a straight path which is the perpendicular bisector of the line segment joining the two floats.

--------------------------------------------------------------------------------------------------------------------------------------------------------------------

(c)

The locus of the police helicopter in pursuit of a car which just passed the junction of two straight roads and which may be on either of them is a line which is the angle bisector of the angle between two roads.

--------------------------------------------------------------------------------------------------------------------------------------------------------------------

(d)

The locus of the treasure buried at the same distance from two intersecting straight roads is the angle bisector of the angle between two roads.

-------------------------------------------------------------------------------------------------------------------------------------------------------

11.3

(a)

The locus of a planet moving at a fixed distance from its sun is a circle of the radius equal the distance of planet from its sun.

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

(b)

The locus of a boat moving at a fixed distance from the coast of a circular island is a concyclic circle to the circular island. (center of the circular island and locus is same)

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

(c)

The locus of the plants laid at a distance of 20ft from a straight row of other plants is a pair of parallel straight lines, either which are 20 ft away from the row of plants and either side of it.

--------------------------------------------------------------------------------------------------------------------------------------------------------------

(d)

The locus of outer extremity of a clock hand is a circle whose radius is same as the lenght of the clock hand.