NCERT Class XI Mathematics - Conic Sections - Solutions
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Question : 65
Total: 71
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
Solution:
Let AOB be the cable of uniformly loaded suspension bridge. Let AL and BM be the longest wires of length 30 m each. Let OC be the shortest wire of length 6 m and LM be the roadway.
Now AL = BM = 30 m, OC = 6 m and
LM = 100 m
∴ LC = CM =
Let O be the vertex and axis of the parabola be y-axis. So, the equation of parabola in standard form isx 2
Coordinates of point B are (50, 24)
Since point B lies on the parabolax 2
∴( 50 ) 2
So, equation of parabola isx 2
x 2
Let length of the supporting wire PQ at a distance of 18 m be h.
∴ OR = 18 m and PR = PQ – QR = h – 6.
Coordinates of point P are (18, h – 6)
Since the point P lies on parabolax 2
∴( 18 ) 2
⇒ 625h = 1944 + 3750 ⇒ h =
Now AL = BM = 30 m, OC = 6 m and
LM = 100 m
∴ LC = CM =
Let O be the vertex and axis of the parabola be y-axis. So, the equation of parabola in standard form is
Coordinates of point B are (50, 24)
Since point B lies on the parabola
∴
So, equation of parabola is
Let length of the supporting wire PQ at a distance of 18 m be h.
∴ OR = 18 m and PR = PQ – QR = h – 6.
Coordinates of point P are (18, h – 6)
Since the point P lies on parabola
∴
⇒ 625h = 1944 + 3750 ⇒ h =
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