Question

A farmer wishes to install 2 hand pumps in his field for watering. The farmer moves in

the field while watering in such a way that sum of distances between the farmer and each hand pump if always 26 meters. Also the distance between the hand pumps in 10

meters

(1) Curve along which the farmer moves?

(ii) Two fixed points where hand pumps are placed

are called

(iii) Find the equation of the curve traced by the farmer

(iv) find the eccentricity of curve along which the farmer moves

(v) What is the radius of the circle having centre at (0./11 ) and passing through

the Foci of the curve along which the farmer moves.​

Answer 1

Given :  A farmer wishes to ins tall 2 hand pumps in his field for watering

The farmer moves in the field while watering in such a way that sum of distances between the farmer and each hand pump is always 26 m

Also the distance between the hand pumps in 10 m

To Find : (1) Curve along which the farmer moves?

(ii) Two fixed points where hand pumps are placed  are called

(iii) Find the equation of the curve traced by the farmer

(iv) find the eccentricity of curve along which the farmer moves

(v) What is the radius of the circle having centre at (0./11 ) and pa ssing through  the Foci of the curve along which the farmer moves.​

Solution:

Curve along which the farmer moves - ELLIPSE

Two fixed points where hand pumps are placed  are called  FOCI

equation of the curve traced by the farmer

distance fixed = 26  => 2a = 26 => a  = 13

Distance between foci = 10  

b² = 13² -(10/2)²  = 12²

=> b = 12

x²/13²  + y²/12²  = 1

x²/a²  + y²/b²  = 1

a = 13  b = 12

e = √(1-b²/a²)

e = 5/12

eccentricity of curve along which the farmer moves = 5/12

radius of the circle having centre at (0 , 11 ) and pa ssing through

the Foci

= √5² + 11²  = √126 = 3√14

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