max area of an isosceles triangle inscribed in an ellipse.

First, it is given that the major axis is along x-axis.

So, coordinates of vertex C are (a, 0).

Now, since, A and B also lies the ellipse and we know that ellipse is symmetrical about x and y axis. So, let coordinates of A and B be (-x1, y1) and (-x1, -y1).

Now, you can find the value of y1 using the equation of the ellipse.

 

So, now you have the coordinates of all the three vertices of triangle.

Using the formula of area of triangle, from coordinate geometry we have calculated the area of triangle ABC.

 

Please note: You must have studied the formula of finding the area of triangle in the chapter of coordinate geometry in class 10.

 

Formula: