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As we have come to know about the meaning of subtangent and subnormal so let’s take an example and get to know how they come into the light. So let y = f(x) and is referred to as that curve which is placed at point P. Then let’s join both the tangent and normal which is P (x, y) to a curve which are the points T and N which are lying on X-axis. The projection points of P which stays the X-axisis M.
 So now, we can easily get the lengths of subtangent and subnormal according to the definition. Here, the length of subtangent is PT and the length of normal is PN and the length of subtangent is TM and the length of subnormal is MN.Â
Carteisian Definition
The cartesian system also definesthe meaning of subnormal and subtangent. Let’s assume that f (x, y) = 0 and the tangent drawn at the point P forms a curve PT and then PN and PA will be referred to as normal of that given point which is perpendicular to X-axis. So here
Polar Definition
Polar also defines the meaning of subtangent and subnormal. Let’s assume that r = f() and when the tangent is being drawn at the point P which leads to forming of a curve PT and then PN and Po which is the normal of that given point and they are perpendicular to the starting or original line OX. So here,
Practical Applications
Some of the practical applications are:
Calculate the equation of tangent and normal relating to the curve x2 = 8y + 6 at the point (0, – 5/4)
Answer:
The equation of the curve is given below:
X2 = 8y + 6
y = (x2-6)/8
Equation of the tangent relating to the curve at (0, -5/4) is dy/dx at this specific point.Â
d y/dx=2x/8=x/4
At (0, -5/4) dy/dx = 0
Tangent’s equation is at (0, -5/4)
y + y1 = m(x – x1)
y + 5/4 = 0(x – 0)
y + 5/4 = 0
Tangent and normal are at vertical positions, this leads to slope of normal = – 1/(dy/dx).
As we know dy/d x = 0 so the normal will be corresponding to y axis and will pass through (0, – 5/4), then the normal’s equation will be (0, -5/4) isÂ
x = 0
Conclusion
As we have concluded we are very clear about the meaning of the subtangent and what subnormal means. We have also learned about the Cartesian definition and the polar definition which very well describes the subtangent and subnormal. The definitions give us an idea that what are the non-similarities between subtangent and subnormal and they give us a chance to us to know about subtangent and subnormal in a better way. The definition helps us find out the formula that helps the sum.
