P(3, 1), Q(6, 5) and R(x, y) are three points such that the angle RPQ is a right angle and the area of ∆RPQ =7, then the number of such points R is

Since the angle RPQ is a right angle,∴ slope of RP × slope of PQ = –1⇒1-y3-x×5-16-3=-1⇒3x+4y=13               (1)Also, area of ∆RPQ = 7⇒12xy1311651=7⇒12x(1-5)-y(3-6)+1(15-6)=±7⇒ – 4x + 3y + 9 = ± 14 ⇒ – 4x + 3y = 5                       (2)and – 4x + 3y = –23                                                      (3)Solving Eq. (1) and (2) and (1) and (3), we get twodifferent coordinates of the point R. So, there are two such points R.