The coordinates of two points A and Bare $$($$ $$3$$, $$4)$$ and (5$$, $$-$$ $$2) respectively. If P is a point not lying on any of the coordinate axes such that PA $$=$$ PB and Area of of ∆PAB $$=$$ $$10$$, then the coordinates of P, are

Question

The coordinates of two points A and Bare $$($$ $$3$$, $$4)$$ and (5$$, $$-$$ $$2) respectively. If P is a point not lying on any of the coordinate axes such that PA $$=$$ PB and Area of of ∆PAB $$=$$ $$10$$, then the coordinates of P, are

Infinity Learn · Accepted Answer

Let the coordinates of P be (x$$, $$y). Then,$$PA=PB$$⇒ $$PA2=PB2$$⇒ (x$$−$$3)2+(y$$−$$4)2=(x$$−$$5)2+(y+2)2x$$−$$3y$$−$$1=0$$                                                                   ...$$(i)Now$$, Area of △$$PAB=10$$⇒ $$12xy13415$$−$$21=$$±$$10$$⇒ $$6x+2y$$−$$26=$$±$$20Solving$$ $$(i) with equations in (ii), we obtain $$x=7$$,$$y=2$$ and $$x=1$$,$$y=0$$.But, P does not lie on any of the coordinate axes. Thus, the coordinates of P are (7$$,$$2)

The coordinates of two points A and Bare ( 3, 4) and (5, - 2) respectively. If P is a point not lying on any of the coordinate axes such that $P A = P B$ and Area of of $∆ P A B = 10$ , then the coordinates of P, are

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The coordinates of two points A and Bare ( 3, 4) and (5, - 2) respectively. If P is a point not lying on any of the coordinate axes such that PA = PB and Area of of ∆PAB = 10, then the coordinates of P, are

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The coordinates of two points A and Bare ( 3, 4) and (5, - 2) respectively. If P is a point not lying on any of the coordinate axes such that $P A = P B$ and Area of of $∆ P A B = 10$ , then the coordinates of P, are