JEE Advance - Mathematics (1979 - No. 20)
(a) Two vertices of a triangle are $$(5, -1)$$ and $$(-2, 3).$$ If the orthocentre of the triangle is the origin, find the coordinates of the third point.
(b) Find the equation of the line which bisects the obtuse angle between the lines $$x - 2y + 4 = 0$$ and $$4x - 3y + 2 = 0$$.
(b) Find the equation of the line which bisects the obtuse angle between the lines $$x - 2y + 4 = 0$$ and $$4x - 3y + 2 = 0$$.
The third vertex of the triangle is $$(-4, -7)$$.
The third vertex of the triangle is $$(4, 7)$$.
The equation of the angle bisector is $$(4 - \sqrt 5 )x + (2\sqrt 5 - 3)y - (4\sqrt 5 - 2) = 0$$.
The equation of the angle bisector is $$(4 + \sqrt 5 )x + (2\sqrt 5 + 3)y - (4\sqrt 5 + 2) = 0$$.
The equation of the angle bisector is $$(4 - \sqrt 5 )x + (2\sqrt 5 - 3)y + (4\sqrt 5 - 2) = 0$$.
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