Question

A bar of given length moves with its extremities on 2 fixed st-lines at right angles.Show that any point on the bar describes an ellipse.

Answer 1

Let the 2 fixed straight lines(OA & OB) be taken as coordinate axis. Let AB be the length of the bar. Let P(x,y) be any point on the bar AB that divides the bar in the ratio a:b

 Draw PL & PM perpendiculars on x and y axis respectively Let the rod AB be inclined at an angle Theta OX i.e angle OAB=theta

then x=PM=bCosTheta and y=PL=aSin theta

Eliminating theta from these equations we get,

x^2/b^2 + y^2/a^2 = 1

Hence the point P(x,y) describes an ellipse.