Muhammad Urd Sher Qaisrani ,

Me and Viera Čerňanová showed you a good answer to your question"

Given in 3D Ellipsoid semi major axis a=5 and b =4 ,c=3 . How can we find the distance D between two focal points (F1 and F2)? "

posted 9 days ago?

I printed a pdf file to show you how to use the Euclidean distance.

But you got silence, didn't respond to answers, and now you are repeating the same question with a little bit change!!

Issam Kaddoura Dear sir i am new user on this research gate so i am not well aware of the proper use of it. I just read your replies and Mr. Viera Cernanova lately. As per my understanding the answer of Mr. Viera is regarding 2D ellipse rather than Ellipsoid. However he also mentioned the sentence (" If a=5, b=4, c=3 is the solid different, but the situation in the plane (F1F2S) is as above. D=6. ") which i didn't understand specially the terminology. I saw the PDF of proof you shared is very helping and nice. I appreciate your help.

Issam Kaddoura I have shared the file named (Details) in this question . In which there are two methods shown. One is using directly from the coordinates of two points and taking the Euclidean distance between them. And the second method is in which firstly we take the Equation of line and then substitute the coordinates of two points. And obtain the value of (x,y,z) with respect to some unknown constant ( t ) which is the measure of the length of that line. After that to substituting the values of (x,y,z) into the equation of ellipsoid x^2/a^2+y^2/b^2+z^2/c^2=1 . As we know the values of a=5, b=4 and c=3. we obtain the value of (t) which is the measure of the length of that line between two points (p0 and p1) . After obtaining (t) we insert it into the equations of (x,y,z) we obtained from equation of line. And getting the values then take the Euclidean distance between P0 and newly obtained (x,y,z) . I have attached the example here.

Now my Question is Should i directly take the Euclidean distance between two points as in Method 1 of the (Details) file . If yes and we have a=5, b=4, c=3 (semi major axis a, and semi minor axis (b , c ) , then how we obtain the distance between two foci ?

If to apply method 2 for distance between (p0 and p1) then again how to obtain distance between two foci ?

Regards

Dear Muhammad Urd Sher Qaisrani ,

I understand that you are a new member. So, if you have asked some question and you got some answers, you need to classify them as helpful or not. If the answer is useful and satisfies your request, the ethics of the RG platform is to recommend the good responses. If you are not satisfied with the answers, you can show your point of view and create a debate with the followers to receive better answers. There is no need to repeat the same question once more, and it is better to stay with the same thread until you get the best solution.

Best wishes

Dear Muhammad Urd Sher Qaisrani ,

There are no foci for the general equation of the ellipsoid.

The foci F1( -D/2,0) and F2( D/2,0) are used only for the ellipse

E: x2 /a2 + y2 /b2 =1, in the plane where (D/2)2 = a2 - b2 .( a < b)

One can easily show that d(F1 , p ) +d(F2 , p) = 2a for any point p belongs to E.

There are no foci for the general equation of the ellipsoid

(EE): x2 /a2 + y2 /b2 + z2 /c2= 1.

We have the following special case: if a > b=c, then we can show

the foci F1( -D/2,0) and F2( D/2,0) work for the whole ellipsoid.

It means d(F1 , p ) +d(F2 , p) = 2a, where p is any point belongs to the ellipsoid(EE);

The proof attached as a pdf file in previous answers.

Your previous method to find the distance between two points

by introducing the parametric equation of the ellipse and the straight line is not practical. Especially, simple and direct methods are available.

PS

There are other symmetric cases for ( a = b < c) and ( a = c < b).

Best regards

Issam Kaddoura Thank you very much sir. your answer is quite helpful. Thanks for the help. Regards

I am not sure whether I understand your figure. Is P1 a point on the y-axis? Then its coordinates should be (0,b,0). But a two-dimensional figure of a three-dimensional configuration is not unambiguous.

Johann Hartl Sir both the P1 and P2 lies on x axis (semi major axis ) at foci of an ellipsoid (oblate). Where y and z axis have equal (y=z) as well as coordinates of P1=(-D/2, 0 , 0) and P2 (D/2, 0,0). Where D is the distance between two foci.

When I look at your figure, it seems to me that P0 and P2 lie on the x axis and P1 lies on the y axisof an xyz coordinate system.