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A curve that passes through (2, 4) and having subnormal of constant length of 8 units can be?
Dear Rishi,
Let the curve be y = f(x). Subnormal at any point = |y*dy/dx|
y*dy/dx = ±8 ;which indicates y dy = ±8dx ;which indicates = ±8x + c
which indicates: y2 = 16 x+2c1,
: c1= -8 or y2 = -16x +2c2,
:c2= 24
Hence : y2 = 16x – 8; y2 = -16x + 24 ;
would be the desired equations.
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length of subnormal =y(dy/dx)
=8 ......(given)
y(dy/dx)=8
y dy = 8 dx
integrating on both sides
y^2 =16x +c (c is integrating constant)
satisfying by (2,4)
we get y^2 = 16(x-1)
this is the equation of required curve.
From,
PRAVIN ULLAGADDI.
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