Find out the tangent line to the parametric curve, Mathematics

Assignment Help:

Find out the tangent line(s) to the parametric curve specified by

X = t5 - 4t3

Y = t2

At (0,4)

Solution

Note that there is actually the potential for more than one tangent line here! We will come across into this more after we're completed with the instance.

Firstly we should do is find the derivative thus we can get the slope of the tangent line.

dy/dx = (dy/dt) / (dx/dt)

= 2t / 5t4 - 12t2

= 2 / 5t3 - 12t        

At this point we have got a little problem. The derivative is in terms of t and all we have acquire is an x-y coordinate pair. After that the next step is to determine the value(s) of t that will give this point. We find out these by plugging the x and y values into the parametric equations and by solving for t.

0 = t5 - 4t3 = t3 (t2 - 4)              ⇒ t = 0, + 2

4 = t2                                             ⇒ t = + 2

It does not matter any value of t which appears in both lists will provide the point. Thus, as there are two values of t that provide the point actually we will get two tangent lines. Though, before we do that let's in fact get the tangent lines.

t = -2

As we already know the x and y-coordinates of the point all that we need to do is find out the slope of the tangent line.

M = dy/dx |t=-2

= - 1/8

The tangent line that is at t  = -2 is then,

Y = 4 - (1/8) x

t = 2

Once again, all we need is the slope.

M = dy/dx |t=2

= 1/8  

The tangent line that is at t = 2 is then,

Y = 4 + (1/8) x


Related Discussions:- Find out the tangent line to the parametric curve

Errors are useful in learning maths, Errors Are Useful :  While teaching c...

Errors Are Useful :  While teaching children, you must have found theft making mistakes off and on. How do you respond to the errors'? What do they tell you about the child-failur

Calculus, how much it cost an hour

how much it cost an hour

Rocks and minerals, question..how do u understand thr rock cycle

question..how do u understand thr rock cycle

Monomial, express the area of a square with sides of length 5ab as monomial...

express the area of a square with sides of length 5ab as monomial

Determine the equation of the tangent line, Determine the equation of the t...

Determine the equation of the tangent line to r = 3 + 8 sinθ at θ = Π/6. Solution We'll first need the subsequent derivative. dr/dθ = 8 cosθ The formula for the deriv

Bussiness, How do these websites help the company strengthen its relationsh...

How do these websites help the company strengthen its relationships with its stakeholders? List the website(s) that you previewed and give examples to support your answers. Who are

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