If the extremities of a line segment of length l moves in two fixed perpendicular straight lines, then the locus of the point which divides this line segment in the ratio 1 : 2 is-

Options

A. a parabola
B. an ellipse
C. a hyperbola
D. None of these

Answer

2

Explanation

Let the two fixed perpendicular straight lines be the co-ordinate axis
let P(h, k) be the point whose locus is required

let PA : PB = 1 : 2
Then PA=`l/3` and PB = `(2l)/3`
`k=l/3sintheta or3k=l sin theta.....(i)`
and `h=(2l)/3costhetaor(3h)/2=lcostheta....(ii)`
Sqauring and adding (i) and (ii) we get
`9k^(2)+(9h^(2))/4=l^(2)`
`therefore` locus `9x^(2)+36y^(2)=4l^(2)`
Which is an eclipse