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Q.

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

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a

2

b

1

c

0

d

4

answer is C.

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Detailed Solution

Since the angle RPQ is a right angle,
 slope of RP × slope of PQ = –1

1-y3-x×5-16-3=-13x+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 two
different coordinates of the point R. So, there are two such points R.

 

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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