Equation of an ellipse
→having center (0,0) , vertex ( and covertex
and focus
is given by:
As definition of an ellipse is that locus of all the points in a plane such that it's distance from two fixed points called focii remains constant.
Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:
Distance from (a,0) to (c,0) is = a-c =
Distance from (-a,0) to (c,0) is = a + c =
a -c + a +c
= a + a
= 2 a →(Option A )
Answer:
The maximum possible length, in centimeters, of the longest piece of rope is 134 cm
Step-by-step explanation:
Let the seven pieces be a,b,c,d,e,f,g
Average of 7 pieces of ropes =68
--A
We are given that the median length of a piece of rope is 84 centimeters.
We arrange the pieces in the ascending order
So, median will be the length of 4th piece
So, d = 84 cm
the length of piece a,b,c will be less than 84 and the value of e,f,g must be greater than or equal to 84
Let us suppose the length of a,b,c be x
Let us suppose the length of e,f be 84
The length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope
So, g = 4x+14
Substitute the value in A
g = 4x+14=4(30)+14=134
Hence the maximum possible length, in centimeters, of the longest piece of rope is 134 cm