Question

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

Answer 1

OX and OY are fixed lines AB is bar, Let point P(x,y) on AB it divides the line AB in a:b draw PM`_|_`OY and PL`_|_`OX
`PM=x=acostheta`
`x/a=costheta`
`PL=y=bsintheta`
`y/b=sintheta`
`cos^2theta+sin^2theta=1`
`(x/a)^2+(y/b)^2=1`
`x^2/a^2+y^2/b^2=1`.