Question

The ends of rod length r move on two mutually perpendicular lines.the locus of point on rod which divides it in the ratio1:1 is

Answer 1

Let the two mutually perpendicular lines be coordinate axes,

Let our point be (x, y)

Let the points at which rod touches the coordinate axes be (x1 ,0) and (0, y1 )

x1²+y1² =r² let us name this equation 1

Also using

x = (mx1 +nx2)/(m+n)

We have

y1 = 2y

x1 = 2x

Using putting values in equation 1 we have,

(2x)²+(2y)²=r²

4x²+4x²=r²

Hope it helps you ❤