A man running a race course notes that the sum of the distances from two flag posts from him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man

Let A(1,2) be a fixed point and 'P' be a variable point in the same plane P moves in the plane in such a way that its distance from A is always a constant. Suppose 'P' is at the point (3,3),find the equation of the path traced by 'P'.

(i)Let A(1,2) be a fixed point and 'P' be a variable point in the same plane.P moves in the plane in such a way that its distance from A is always a constant.Suppose 'P' is at the point (3,5).Find the equation of the path traced by 'P'.

A girl standing on a lighthouse built on a cliff near the seashore, observes two boats due East of the lighthouse. The angles of depression of the two boats are 30^@ and 60^@ . The distance between the boats is 300 m:-Find the distance of the top of the lighthouse from the sea level.(Boats and foot of the lighthouse are in a straight line).

Find the equation of the set of points P, the sum of whose distances from A (4,0,0) and B (-4,0,0) is equal to 10.