Question 1157836
Let the vertex be at the point ( 0, 0 )
The parabolic cables are connected
to towers at ( 400, 100 ) and ( -400, 100 )
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You need to find {{{ y[1] }}} at points 
( 200, y[1] ) and ( -200, y[1] )
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The form is:
{{{ y = a*x^2 + b*x + c }}}
At ( 0, 0 )
{{{ 0 = a*0^2 + b*0 + c }}}
{{{ c = 0 }}}
At ( 400, 100 )
{{{ 100 = a*400^2 + b*400 }}}
{{{ 100 = 160000a + 400b }}}
(1) {{{ 1600a + 4b = 1 }}}
At ( -400, 100 )
{{{ 100 = a*(-400)^2 + b*( -400 ) }}}
{{{ 100 = 160000a - 400b }}}
(2) {{{ 1600a - 4b = 1 }}}
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Add (1)and (2)
(1) {{{ 1600a + 4b = 1 }}}
(2) {{{ 1600a - 4b = 1 }}}
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{{{ 3200a = 2 }}}
{{{ a = 1 / 1600 }}}
and
(1) {{{ 1600a + 4b = 1 }}}
(1) {{{ 1600*( 1/1600 ) + 4b = 1 }}}
(1) {{{ 4b = 0 }}}
(1) {{{ b = 0 }}}
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The equation is:
{{{ y = ( 1/1600 )*x^2 }}}
At ( 200, y[1] )
{{{ y[1] = ( 1/1600 )*200^2 }}}
{{{ y[1] = 40000 / 1600 }}}
{{{ y[1] = 25 }}}
( you get the same result at ( -200, y[1] ) )
The height of the cables at a point 
200 meters from the center is 25 m
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check the math & get a 2nd opinion if needed



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