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what is the lenght of subtangent in the term of differential quotients of any general curve...

what is the lenght of subtangent in the term of differential quotients of any general curve...

Grade:12

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
8 years ago
Let tangent and normal to a parabola at a point P(x1,y1) be extended to meet the axis of the parabola at N and T respectively.

PT is termed the length of the tangent.
PN is termed the length of the normal.

Drop a perpendicular to the axis from the point P and call it PP'.

P' T = subtangent
P’ N = subnormal

If the tangent makes an angle of ψ with the axis


length of the subtangent = y1 cot ψ = y1/(dy/dx)

dy/dx =tan ψ = 2a/y1 = m (slope of the tangent)
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