Items tagged with circle

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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?


I want to calculate the intersection between three circles.
I know that in this case i can calculate intersection of only the first and second equation, but I need this for a interactive component.

The command "intersection"[GEOMETRY] work only with 2 circles.

I did this but it doesn't work.


Parametric equation of a circle in 3d by three points. Draghilev method.


In some cases when dealing with vectofields an such the are integral has to be expressed in terms of r(t).

the general form for r is r^2=(r*cos(t)-a)^2+(r*sin(t)-b)^2, When I solve this in maple it seems like I get the inverse of the desired result.

If I knew that was always the case I could just inverse my result to get the right expression for r, but im not sure if it only applies for this particular cas or all cases.

I would be happy if anyone took a quick look and suggested a way to obtain the desired solution for any center (a,b) for the circle.



Expression for radius, circle centred at (a,b)

RA := r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2

r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2


isolate(r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2, r)

r = (1/2)*(a^2+b^2)/(cos(t)*a+b*sin(t))


eval(%, [a = -1, b = 0])

r = -(1/2)/cos(t)


plot3d([-2*x, x^2+y^2], y = -sqrt(-x^2-2*x) .. sqrt(-x^2-2*x), x = -2 .. 0, color = [green, red], orientation = [0, 0, 0])


(1/2)*Pi <= t and t <= 3*Pi*(1/2)

(1/2)*Pi <= t and t <= (3/2)*Pi


0 <= r and r <= -2*cos(t)

0 <= r and r <= -2*cos(t)


Area_off_center = int(r, [r = 0 .. -2*cos(t), t = (1/2)*Pi .. 3*Pi*(1/2)]); 1; Area_at_center = int(r, [r = 0 .. 1, t = 0 .. 2*Pi])

Area_off_center = Pi


Area_at_center = Pi






I would also happily like to know how I can solve for the range r can take, obviously in the example i´m working with here r starts at 0, but that is not always the case i guess.


Thank you, your help is much apperciated

how to Prove that the circumference of a circle of radius r is 2πr
on maple ?????

Suppose I have the parametric equations of a circle



where t runs from 0 to 2*pi. How can I show the orientation of this parametric curve on a plot?

Dear all,

I want to plot for example cos(theta) from 0 to 2*Pi inside a circle at a radius R. The axis theta of the ploted function is at a radius R.

Is it possible ?


i want to plot a circle which is centered at(0,0),and the radius is the length of Point2 and origin

but it shows some error,how could i do to solve this

i want to plot a circle with that centered at (0,0),and the radius is the length of Point2 and orgin

but it shows the error

how could i do to solve this









c1 := circle([0, 0], 1, color = red);
p2 := implicitplot(x = 1/2, x = -2 .. 2, y = -1 .. 1.1, colour = blue, linestyle = 1, thickness = 2);
display(c1, p2);

How to fill that part beetween line and circle(where x>1/2 in circle )?

"Circular segment" is the unfortunate but standard term for the region between a chord and an arc of a circle sharing the same endpoints (see  I say "unfortunate" because the phrase suggests a line segment when it actually means a planar region.

I would like to plot a shaded circular segment using Maple17.  I want the endpoints of the chord & arc to be anything I please, so the chord is not necessarily horizontal, or vertical, or the diameter of the circle, etc.

At the URL

there is an image containing a shaded circular segment, but I don't see what code produced the image.  The image there includes a horizontal chord, and I don't know if the code used to produce that image can be adapted for chords that are not horizontal.

If I have to, I can plot a shaded polygon with a huge number of sides that is indistinguishable from a circular segment.  I have plotted polygons before.  But it would obviously be preferable to plot a shaded circular segment.

If there a way to plot two curves of the form r = f(theta) and shade the region between them?  This would be better than the huge-polygon approach, but not as good as a simple command for plotting a shaded circular segment, if such a command exists.

In 2D, graph a blue ellipse x(t)=3cos(t), y(t)=2sin(t) for 0≤t≤2∏. For t=0.5 graph a green tangent line to the ellipse and a red osculating circle. Also, give the curvature, the equation of the tangent line and the center of the osculating circle

I think i'm missing something easy her , but I am trying to plot a circle and cannot figure out

what I am doing wrong. The equation for the circle is:


I define the equation

c := x^2+(y-3)^2 = 25

Solve it for y so I should be able to plot it with plot(cplot); :

cplot:=solve(c, y)

But what I get as answer is:

3+sqrt(25-x^2), 3-sqrt(25-x^2)

The equation of the circle is part of a homework assignment,...

I can't solve probably very easy problem. How to plot a filled semicircle which is rotated across one axis by an angle alpha? I came to the solution which I don't consider as the best one (since e.g. it will not work for alpha=Pi/2*(odd integer)) and I believe someone of you will show me a better approach. Thank you in advance.

My solution:

alpha := (1/6)*Pi:
plot3d([x, y, y*tan(alpha)], x = -1 .. 1, y = 0 .. sqrt(1-x^2)*cos(alpha), axes = normal, labels = ["x", "y", "z"...

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