Question

The ends A , B of a straight line segment of constant length c slide upon the fixed rectangular axes OX ,OY respectively. If the rectangle OAPB be completed- then show that the locus of the foot of the perpendicular drawn from P to AB is

x2/3 + y2/3 = c2/3

Answer 1

Let OA = a and OB = b. Then, the coordinates of A and B are(a,0) and (0, b)respectively and also, coordinates of P are (a, b). Let θ be the foot of perpendicular from P on AB and let the coordinates of Q(h, k). Here, a and b are the variable and we have to find locus of Q.

Given AB = c

On solving Eqs. (ii) and (iii), we get

Hence, locus of a point is x2/3 + y2/3 = c2/3