I've found out that the curve is a closed figure and . Now, we need to find the lines that join (0,0) and (12,16) and are tangent to the curve. Not able to move further. help!! We can find the equations of the lines that pass through (0,0) and (1,8), and (12,16) and the topmost point of the figure. Their point of intersection will give us the co-ordinates of the point.Then finding distance is simple.
The equation is a circle with center at (6,8) and radius 5. So the only possible shortest distance satisfying the given condition must be sum of lengths of two tangents (one from [0,0] and other from [12,16]) and then extending the tangent to intersect each other. radius = 5 and distance from origin to center = 10. Therefore length of Tangent PT^2 = 10*(10-5) => PT = 5(2)^1/2. The 4 tangents when joined results in a parallelogram circumscribing the given circle. Also one of the angles of the parallelogram would be 60 as Perpendicular = 5, Hypotenuse=10. The other would be 120.
Distance = 10{3*sqrt(2)+sqrt(3)}/3 = 19.91 Approx. Ans.
I've found out that the curve is a closed figure and . Now, we need to find the lines that join (0,0) and (12,16) and are tangent to the curve. Not able to move further. help!!
ReplyDeleteWe can find the equations of the lines that pass through (0,0) and (1,8), and (12,16) and the topmost point of the figure. Their point of intersection will give us the co-ordinates of the point.Then finding distance is simple.
hmmm, you were on right track till, you did some mistake !
ReplyDeleteThe equation is a circle with center at (6,8) and radius 5. So the only possible shortest distance satisfying the given condition must be sum of lengths of two tangents (one from [0,0] and other from [12,16]) and then extending the tangent to intersect each other.
ReplyDeleteradius = 5 and distance from origin to center = 10. Therefore length of Tangent PT^2 = 10*(10-5) => PT = 5(2)^1/2.
The 4 tangents when joined results in a parallelogram circumscribing the given circle. Also one of the angles of the parallelogram would be 60 as Perpendicular = 5, Hypotenuse=10. The other would be 120.
Distance = 10{3*sqrt(2)+sqrt(3)}/3 = 19.91 Approx. Ans.
10+5pi .. right ??
ReplyDeletewhat is the correct answer outtimed and wats the best method?
ReplyDeletethe given curve is a circle with center at (6,8) and radius = 5.
ReplyDeleteis the shortest path = 17 + 5*pi/2 .