Question

a necklace hanging from two fixed points A and B at the same level. the length of the necklaces between two points is 100cm. the midpoint of the necklace is 8 cm below A and B. assume that the necklaces hang in parabolic curve , find the equation of the curve ( solution )

Answer 1

Let us assume that the necklace is hanging like shown below in the figure,
the two points where the parabola(or necklace)meets the x axis is kept (0,0) and(100,0)to ensure distance as 100 between A and B.Then two points certainly lie on that parabola,as shown which are (50,-8) and (100,0).....this we put in standard parabola equation:y=a*x^2+x*b
Two coordinates;
x = 50, y = -8
50^2a + 50b = -8
2500a + 50b = -8
and
x = 100, y = 0
100^2a + 100b = 0
10000a + 100b = 0
:
Multiply the 1st equation by 2, subtract from the 2nd equation


10000a + 100b = 0
5000a + 100b = -16
---------------------subtraction eliminates b find a
5000a = 16
a = 16/5000
a = 0.0032
:
Find b
2500(0.0032) + 50b = -8
8 + 50b = -8
50b = -8 - 8
b = -16/50
b = -0.32
which finally gives the equation of parabola as
y = 0.0032x^2 - 0.32x

Answer 2

thanks...

Answer 3

welcome,but did u understand the solution fully?ask if there are still doubts...