Tangents with parametric equations - polar coordinates, Mathematics

Assignment Help:

Tangents with Parametric Equations

In this part we want to find out the tangent lines to the parametric equations given by

X= f (t)

Y = g (t)

To do this let's first remind how to find the tangent line to y = F(x) at x=a. now here the tangent line is illustrated by,

301_Tangents with Parametric Equations - polar coordinates.png

Now here, Note that if we could make out how to get the derivative dy/dx from the parametric equations we could just again use this formula as we will be capable to make use of the parametric equations to find out the x and y coordinates of the point.

Thus, just for a second let's assume that we were able to eliminate the parameter from the parametric form and write the parametric equations in the type y = F (x).

Now here, plug the parametric equations in for x and y. Yes, it look like silly to remove the parameter, after that immediately put it back in, but it's what we require to do to get our hands on the derivative. Doing this provides,

g (t) = F (f (t))  

Now, distinguish with respect to t and notice that we'll require to make use of the Chain Rule on the right hand side.

g' (t) = F' (f(t)) f' (t)

Let us do other change in notation.  We require to be careful along with our derivatives here. Lower case function's derivatives are regarding to t when derivatives of upper case functions are with respect to x.  Thus, to ensure that we keep this straight let's rewrite things like this.

dy/dt = F' (x) dx/dt

At this point we should recall ourselves just what we are after.  We required a formula for that is in words of the parametric formulas. 

Note: though that we can obtain that from the exceeding equation.

dy/dx = (dy/dt) / (dx/dt) ,         given dx/dt ≠ 0

Notice also that this will be a function of t and not x.


Related Discussions:- Tangents with parametric equations - polar coordinates

Find the distance of the journey, A train covered a certain distance at a u...

A train covered a certain distance at a uniform speed.  If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time.   And if the train were

Hypothesis testing, Hypothesis Testing Definition of Hypothesis Testing...

Hypothesis Testing Definition of Hypothesis Testing - A hypothesis is a claim or an opinion about an issue or item.  Hence it has to be tested statistically in order to esta

Area related to circle, If ABCD isaa square of side 6 cm find area of shad...

If ABCD isaa square of side 6 cm find area of shaded region

Parallel vectors - applications of scalar multiplication, Parallel Vectors ...

Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections.  Two vectors are parallel if they have

Permutation, Permutation - It is an order arrangement of items whether...

Permutation - It is an order arrangement of items whether the order must be strictly observed Illustration Assume x, y and z be any of three items. Arrange these in all

Compound and simple interest, Your grandparents gave you a gift of R2 000 o...

Your grandparents gave you a gift of R2 000 on your 16th birth day. You want to invest the money in an account over four years. You have an option of investing the R2 000 at 8% per

Find the z-score, For a population with a mean of μ=80 and a standard devia...

For a population with a mean of μ=80 and a standard deviation of o=12, find the z-score corresponding to each of the following samples. a.    M=83 for a sample of n=4 scores b.

Partial Differentiation, If the sides angles of a triangle ABC vary in such...

If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0

Prove that ar= 3/7 ac of parallelogram , ABCD is a parallelogram in the giv...

ABCD is a parallelogram in the given figure, AB is divided at P and CD and Q so that AP:PB=3:2 and CQ:QD=4:1. If PQ meets AC at R, prove that AR= 3/7 AC. Ans:    ΔAPR ∼ Δ

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd