Question

The subnormal of the piarabola $y^{2}=4 a x$ is

   The subnormal of the piarabola $y^{2}=4 a x$ is

Higher Engineering Mathematics

Higher Engineering Mathematics

Grewal B.S. 42nd Edition

Chapter 4, Problem 27

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Solved by Expert Jeff Vermeire

04/08/2022

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The given equation is $y^{2}=4 a x$. Show more…

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The subnormal of the piarabola $y^{2}=4 a x$ is

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Key Concepts

Parabola

A parabola is a conic section that is defined as the locus of all points equidistant from a fixed point (the focus) and a fixed line (the directrix). In analytic geometry, its standard equation (when the axis of symmetry is horizontal) is often given as y² = 4ax, showing the relationship between the geometric properties and the algebraic representation of the curve.

Normal Line

The normal line to a curve at a given point is the line perpendicular to the tangent at that point. In the context of calculus and analytic geometry, determining the normal line involves calculating the derivative to find the slope of the tangent first, and then using the negative reciprocal of that slope for the normal. The concept is fundamental in understanding how curves behave locally.

Subnormal

The subnormal is the projection of the segment of the normal line, drawn from the point of contact with the curve to the x-axis, onto the x-axis itself. It represents a specific measure that relates the geometry of the curve to its tangent and normal lines, and is typically computed using the derivative, linking its value to the parameters of the curve.

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