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Calculus help please?-will award best answer!?
1. Consider the circle given by the equation:
(x − 1)^2 + (y − 2)^2 = 4.
(a) Determine the point(s) on the circle where the tangent line is horizontal.
(b) Determine the point(s) on the circle where the tangent line is vertical.
2. Two radar stations located at points A and B, where point B is 6 km east of point A, are tracking a ship (north east of A). Suppose that the distance between the ship and A is increasing at the rate of 28 km/h when the ship is 5 km from A. At this same instant, the ship is also 5 km from B, and the distance between them is increasing at 4 km/h. How fast is the ship moving at that instant?
Please explain how you got the answers so I may use this to study!
2 Answers
- Mike GLv 73 years agoFavourite answer
1) a) x^2-2x+1+y^2-4y+4 = 4
2x-2 +2y dy/dx - 4 dy/dx = 0
2x-2 + (2y-4) dy/dx = 0
x-1 + (y-2) dy/dx = 0
dy/dx = (1-x)/(y-2)
0 = (1-x)/(y-2)
0 = 1-x
x = 1
y-2 = ±2
y = 0 or 4
Points are (1,0) and (1,4)
b) (y-2)/(1-x) = 0
y = 2
x-1 = ±2
x = -1 or 3
Points are (-1,2) and (3,2)
See graph
- Steve ALv 73 years ago
A) radius = 2
Center = (1,2)
Horizontal at center +/- radius (1,0) and (1,4)
Vertical at (3,2) and (-1,2)
