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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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thanks and regards.


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.


 


 

7 years ago
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