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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. askIITians.com provides online iit jee courses and IIT JEE Test Series with IITians. Click here to get free online test series and check your status timely or you can join us as our registered user for getting best iit jee study material or iit jee test series. Click here to find IIT JEE Packages or course details with askIITians. for further details visit the folowing links: http://www.askiitians.com//iit-jee-online-coaching.aspx http://www.askiitians.com/iit-jee-test-series.aspx http://www.askiitians.com/iit-study-material/ Askiitians provide you all the best possible information, feel free to ask. all the best. thanks and regards. Akhilesh Shukla
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.
askIITians.com provides online iit jee courses and IIT JEE Test Series with IITians. Click here to get free online test series and check your status timely or you can join us as our registered user for getting best iit jee study material or iit jee test series.
Click here to find IIT JEE Packages or course details with askIITians.
for further details visit the folowing links:
http://www.askiitians.com//iit-jee-online-coaching.aspx
http://www.askiitians.com/iit-jee-test-series.aspx
http://www.askiitians.com/iit-study-material/
Askiitians provide you all the best possible information, feel free to ask.
all the best.
thanks and regards.
Akhilesh Shukla
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.
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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