<PRE><B>Question 639442</B>
A necklace hanging between two fixed points A and B at the same level.
 The length of the necklace between the two points is 100cm.
 The midpoint of the necklace is 8cm below A and B.
 Assume that the necklace hangs in the form of parabolic curve,
 find the equation of the curve.
:
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 = .0032
:
Find b 
2500(.0032) + 50b = -8
8 + 50b = -8
50b = -8 - 8
b = -16/50
b = -.32
:
The equation: y = .0032x^2 - .32x
Which looks like
{{{ graph( 300, 200, -30, 120, -8, 10, .0032x^2-.32x) }}} 
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