Let PQR be a $$right-angled$$ isosceles triangle, right angled at $$P(2$$,$$1)$$. If the equation of the line QR is $$2x+y=3$$,then the equation representing the pair of lines PQ and PR is

Question

Let PQR be a $$right-angled$$ isosceles triangle, right angled at $$P(2$$,$$1)$$. If the equation of the line QR is $$2x+y=3$$,then the equation representing the pair of lines PQ and PR is

Infinity Learn · Accepted Answer

Let m be the slope of |PQ. Then, $$tan$$  $$450=$$|m−$$($$−$$2)1+m($$−$$2)$$|$$=$$|$$m+21$$−$$2m$$|∴$$m+2=1$$−$$2m$$ or −$$1+2m=m+2$$∴$$m=$$−$$13or$$ $$m=3Hence$$, the equation of PQ isy−$$1=113(x$$−$$2)or$$ $$x+3y$$−$$5=0$$ and the eqation  of PR $$ism1+11$$−$$m1=$$$$tan$$ α$$=$$−$$1$$−$$m21$$−$$m2or$$ $$m1+m2=($$$$tan$$ α−$$1)2+($$$$tan$$ α$$+1)2tan2$$α−$$1$$ −$$2sec2$$α×$$cos2$$α$$cos$$ $$2$$α∴−$$2$$ $$sec$$ $$2$$α$$=$$−$$2hor$$ $$cos$$ $$2$$α$$=1hor$$ $$2cos2$$α−$$1=1h$$ $$cos$$α$$=1+h2h$$  and α$$=h+1h$$−$$1y$$−$$1=3(x$$−$$2)$$ or $$3x$$−y−$$5=0$$ Hence, the combined equation of PR and PR $$is(x+3y$$−$$5)(3x$$−y−$$5)=0$$ or $$3x2$$−$$3y2+8xy$$−$$20x$$−$$10y+25=0$$

Let PQR be a right-angled isosceles triangle, right angled at P(2,1). If the equation of the line QR is 2x+y=3,then the equation representing the pair of lines PQ and PR is

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