The length of subnermal to the curve y=x^2 at (2, b) is (a) 28 (b) 32 (c) 96 (d) 64 .

Name: Problem 10, Chapter 4: Higher Engineering Mathematics
Uploaded: 2019-07-18T03:19:49-08:00
Duration: 7 min 25 s
Channel: Carlos Pinilla
Description: The length of subnermal to the curve y=x^2 at (2, b) is (a) 28 (b) 32 (c) 96 (d) 64 .

step 1 So perhaps by some reason in life you ask yourself what is the length of the path given by two -

The length of subnermal to the curve y=x^2 at (2, b) is (a)...

Key Concepts

Normal Line

The normal line at a point on a curve is the straight line that is perpendicular to the tangent line at that point. Its slope is the negative reciprocal of the tangent’s slope. The normal line is used in various geometrical constructions on the curve, including finding its intersection with the coordinate axes, which in turn leads to the determination of distances like the subnormal.

Subnormal

The subnormal is the projection on the horizontal axis of the segment of the normal line between the point on the curve and its intersection with the x?axis. It is derived by finding the x-intercept of the normal line, and its length is closely related to both the function value and its derivative at the chosen point. This concept is an application of differential calculus in the geometric analysis of curves.

Derivative

The derivative of a function is the fundamental concept that measures the rate at which the function’s output changes with respect to its input. In the context of curves, it gives the slope of the tangent at any given point, which is key to understanding and computing various line segments associated with the curve, such as the tangent, normal, subtangent, and subnormal.

Tangent Line

A tangent line to a curve at a particular point touches the curve without crossing it (locally) and has the same slope as the curve at that point. Knowing the equation of the tangent line, obtained using the derivative, allows one to determine where this line intersects coordinate axes, a process that is essential when deriving the lengths of projections such as the subtangent or the subnormal.

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