Grade 12Differential Calculus
what is the lenght of subnormals in the term of differential quotients of any general curve...
what is the lenght of subnormals in the term of differential quotients of any general curve...
1 Answer
Vijay Mukati
Dear Student,
Let P(x,y) be any point on any general curve. PG be a normal to the curve at point P and G be the point of axis axis. Let PN be the lilne perpendicular to x-axis. So the Projection of Tangent (PG) on the x-axis (NG) is the length of subnormal. Now if PT is tangent at P and T be on x-axis. So concider Angle NTP = theta = angle GPN. Therefore, The length of subnormal will be NG = y tan (theta).
Thanks.
Let P(x,y) be any point on any general curve. PG be a normal to the curve at point P and G be the point of axis axis. Let PN be the lilne perpendicular to x-axis. So the Projection of Tangent (PG) on the x-axis (NG) is the length of subnormal. Now if PT is tangent at P and T be on x-axis. So concider Angle NTP = theta = angle GPN. Therefore, The length of subnormal will be NG = y tan (theta).
Thanks.
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