Write a user-defined function that plots an ellipse with axes that are parallel

Question

Write a user-defined function that plots an ellipse with axes that are parallel to the x and y axes, given the coordinates of two vertices and another point that the ellipse passes through. For function name and arguments, use ellipseplot(A, B, C). Here A and B are 2-element vectors containing vertex coordiates and C is a 2-element vector containing coordinates of the other point on the ellipse. Use the function to plot the ellipses containing these points. (a) A (2, 3), B (11, 3), C(10, 4) (b) A (2, 11), B(2, -4), C(4, 8)

Explanation / Answer

Solution: (a)

The general equation of ellipse in 2D can be written as

     ………………………(1)

By using given three points here we will find out the coefficients of

Now we will form a matrix by using the three points and given by

      …………………….(2)

In our given problem the three points and are given by respectively.

Therefore using equation (2) we have

      …………………….(3)

Now we solve system of equations (3) by matrix inversion method.

Therefore      

              

  and

Now the angle of inclind of the ellipse by

Now we know that

and

Therefore semi major axis

And semi minor axis

Therefore the equation of the ellipse is

If we put the values of and then we will get the required equation of the ellipse.

Solution: (b)

Same as solution (a)

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