A curve that passes through (2, 4) and having subnormal of constant length of 8 units can be?

rishi khare Grade: 12

        A curve that passes through (2, 4) and having subnormal of constant length of 8 units can be?

7 years ago

Answers : (2)

Kevin Nash

askIITians Faculty

332 Points

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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Akhilesh Shukla

7 years ago

Pravin Prabhuling Ullagaddi

18 Points

										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.