On solving a problem I came across the last day, this is what has happened:
Problem:
Let A(–1, 0) and B(2, 0) be two points on the x-axis. A point 'M' is moving in xy-plane (other than x-axis) in such a way that angle MBA = 2 times angle MAB, then the point 'M' moves along a conic. Find the conic.
My solution:
Consider the given data that angle MBA is twice angle MAB. Using sine rule in order to get a relation between the distances MA and MB, we eventually get a circle.
(Sorry for the inconvinience of not being able to provide a diagram.)
The given solution:
Both the methods seem right in their own way, but the final answers are completely different. How can this be explained?