If the lines represented by the equation $$3y2$$−$$x2+23x$$−$$3=0$$ are rotated about the point (3$$,$$0) through an angle of $$150$$, one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

Question

If the lines represented by the equation $$3y2$$−$$x2+23x$$−$$3=0$$ are rotated about the point (3$$,$$0) through an angle of $$150$$, one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

Infinity Learn · Accepted Answer

The given equation of the pair of straight lines can be rewritten as (3$$ y−$$x+3)(3$$ $$y+x$$−$$3)=0Their$$ separate equations are $$3y$$−$$x+3$$ $$=0$$ and $$3y+x$$−$$3$$ $$=0or$$ $$y=13x$$−$$1$$ and $$y=$$−$$13x+$$−$$1$$ or $$y=($$$$tan$$ $$300)x$$−$$1$$ and $$y=($$$$tan$$ $$1500)x+1After$$ rotation through an angle of $$150$$ as given in the question, the lines are $$(y$$−$$0)=$$$$tan$$ $$450(x$$−$$3) and $$(y$$−$$0)=$$$$tan$$ $$1350(x$$−$$3)or$$ $$y=x$$−$$3$$ $$y=$$−$$x+3$$ Their combined equation is $$(y$$−$$x+3)(y+x$$−$$3)=0or$$ $$y2$$−$$x2+23x$$−$$3=0$$

If the lines represented by the equation 3y2−x2+23x−3=0 are rotated about the point (3,0) through an angle of 150, one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

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