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
Answers
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
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
Learn More:
area enclosed within the ellipse 5x^2 + 2y^2 =80 is ??? - Brainly.in
https://brainly.in/question/22650505
Equation of an ellipse is x2+ y2+ xy + 1 = 0. (1) Length of largest ...
brainly.in/question/3103321
Consider an ellipse whose center is at the origin and it's major axis ...
brainly.in/question/7159663
