## System of linear equations...

I have to find the tangent lines to the circle x^2+y^2+6*x-8*y+25 = 1/16 which pass at the O(0;0)

So i make a general line y=m * x

Ho can i put m*x instead of y in the circle and calculate the delta of the equation that i get?

## Tangent Field in Maple...

The question explores the family of differential equations dy/dx = sqrt(1+(a*x)+(2*y)) for various values of the parameter a.

This figure shows the tangent field in the case a=1.

sketch a tangent field in the case a=-2.

need the following diagram on maple:

## Tangent to a curve in maple...

A family of curves has polar equation r=cos^n (theta/n), 0<=theta,n*pi, where n is a positive even integer.

Previously Using t = theta as the parameter and finding  a parametric form of the equation of the family of curves it was shown that

dy/dx = (sin(t)sin(t/n)-cos(t)cos(t/n)) /( sin(t)cos(t/n)+cos(t)sin(t/n)).

Is it possible to show on Maple with a program that there are n+1 points where the tangent to the curve is paralell to the y axis?

## Find angle between curves...

How to get tangent angle between two curves?

example for these : f(x)=((x^4+5)^(1/2))/(sinx+5) and g(x)=cosx^2   ; x>0

thanks :)

## How to draw vector field on sphere?...

i guess that it is this.

actually my goal is

drawing

tangent vector field on even-dimensional n-spheres

can vector field plot do this too?

if start from draw vector field on a sphere

i find that intersectplot under plot,

is it possible for fieldplot has this

such as the graph in wiki

https://en.wikipedia.org/wiki/Hairy_ball_theorem

## How to plot tangent line?...

Write a Maple procedure which takes any cubic polynomial [−3, 3] p −→ R and returns the following:

How i can plot of p and its tangent lines illustrating the nature of each critical point.

Demonstrate this in the instance that p(x) = 1/3 x^ 3 − 6/10 x^ 2 − 187/100 x + 1.

Any ideas how i can solve this?

## Why do these commands succeed?...

From a Maple Primes answer two years ago:

f(x,y) is the equation of a line through point [m,n]. The solve command finds values of a and b for which f(x,y) are lines through [m,n] and tangent to x^2 + y^2 = r^2.

f := proc (x, y) options operator, arrow; a*(x-m)+b*(y-n) end proc

solve([f(0, 0) = r, a^2+b^2 = 1], [a, b])

These commands are far from the conventional solution. Why do they provide the correct answers?

## Acceleration components

Maple 2015

As a very good application for viewing and calculation of the components of acceleration either tangential or normal. Besides immediately it is shown an Application for physics.

Componentes_de_la_Acelelación.mw

(in spanish)

L. Araujo C.

## How to plot the tangent line of a equation given a...

Hi, I am stumped I've tried many ways but end up getting a graph with nothing on it or errors. I am trying to plot the tangent line to the equation f(x) = 2cosx-x^2 at x = 2; In addition, how would I plot the tangent line and the equation on one graph with distinctive line pattern for example, one being blue and dotted, while the other being red solid).

## How can I plot the whole curves by odeplot?...

Dear All，

I solve an equation  as follows,

m:=dsolve({T(0) = 300, diff(T(t), t) = (min(G1, G2)-Loss)*(1/35513)}, T(t), numeric)

G1,G2, and Loss are functions of T and G1 and Loss are tangent at point A where T=600, when I　want to plot the dsolve solution by odeplot,like this

odeplot(m, [t, T(t)], 0 .. 800)]

I got a curve whose maximum value  is  600( equal to the tangent value) and actually the value should increase after passing the tangent point, Who can tell me where is the problem. Thanks.

## how do you insert a tangent line onto a graph or m...

I need to make two graphs.  1st take the equation y= ln3x+3 and graph it and it's derivative.  Then find the equation of the tangent line and the normal line to the given function at x=e   Then I need to create a single graph containing the function, the tangent line, and it's normal line.  Any pointers or help would be greatly appreciated.  I can graph the equation and it's derivative ok but I don't know how to make a graph with multiple stuff on it.  Thanks

## How can I plot the tangent line in polar coordinat...

with(plots):

a:=polarplot(3-3*cos(theta),theta=0..2*Pi):

c:=plot((3*sqrt(2)+3)/2 + ((-3*sqrt(2))/(-3*sqrt(2)-6))*(x+((3*sqrt(2)+3)/2)),x=-10..10):

display(a,c,view=[-10..10,-10..10]);

a:= is the polar plot of the cardiod (3-3cos(theta)

In order to plot the tangent line to the cardiod in theta= 3Pi/4, I find the point (x,y) in rectangular coord x=(3-3cos(theta)cos(theta) and y=(3-3cos(theta)sin(theta); then I find the derivative of dx/dy=

[(3-3*cos(theta)*cos(theta)+sin(theta)(3sin(theta)]/[-(3-3cos(theta)sin(theta)+cos(theta)(3sin(theta)]and from here I get the slope.So I can plot c:= tangent line to the cardiod in 3Pi/4.

How can I avoid having to convert everyting to rectangular coords, and plot the tangent line in polars?

## How to select two lines (not perpendicular) from a...

I want to find a point has coordinates are integer numbers and write the equation of tangent line to a given circle,  knowing that, the points of tangent has also integer coordinates. For example, the circle has centre M(-1,-5) and radius R=5. I tried

restart:

with(geometry):

point(M,-1,-5):

R:=5:

eqS:=Equation(circle(S,(a-HorizontalCoord(M))^2 + (b-VerticalCoord(M))^2 -R^2=0,[a,b],'centername'=T)):

L:=[]:

for a from -50 to 50  do

for b from -50 to 50  do

if  a <>HorizontalCoord(M) and b<>VerticalCoord(M) and eqS then

L:=[op(L), [a,b]] fi;

od: od:

nops(L);

eqS:=Equation(circle(S,(x-HorizontalCoord(M))^2 + (y-VerticalCoord(M))^2 -R^2=0,[x,y],'centername'=T));

k:=[seq](sort(Equation(TangentLine(P, S, point(A, pt[])), [x,y])), pt in L):

seq([L[i],k[i]],i=1..nops(L));

Next,

> with(combinat):

d:=choose(k,2):

for i from 1 to nops(d) do

seq([d[i],solve([op(1,d[i]),op(2,d[i])],[x,y])],i=1..nops(d));

end do;

If I want to the point of intersection of two lines which are not perpendicular line, for example

[[-3*x-4*y-48 = 0, 4*x+3*y-6 = 0], [[x = 24, y = -30]]]

How can I select?

## Why is there an error in Tangent command?...

Why does:

Student[Calculus1]:-Tangent(tan(3*x)-5*exp(-x^3),x=0,output=plot,gridlines=true,caption="")

produce the following error?

Error, (in plots:-display) integer or integer range expected in op list