$$P(3$$, $$1)$$, $$Q(6$$, $$5)$$ 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

Question

$$P(3$$, $$1)$$, $$Q(6$$, $$5)$$ 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

Infinity Learn · Accepted Answer

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.

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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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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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