1

IIT-JEE 1983

Subjective
The vertices of a triangle are
$$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3},a\left( {{t_2} + {t_3}} \right)} \right],\,\,\left[ {a{t_3}{t_1},\,a\left( {{t_3} + {t_1}} \right)} \right]$$. Find the orthocentre of the triangle.

Answer

$$\left( { - a,a\left( {{t_1} + {t_2} + {t_3}} \right) + a{t_1}{t_2}{t_3}} \right)$$
2

IIT-JEE 1980

Subjective
A straight line $$L$$ is perpendicular to the line $$5x - y = 1.$$ The area of the triangle formed by the line $$L$$ and the coordinate axes is $$5$$. Find the equation of the Line $$L$$.

Answer

$$x + 5y - 5\sqrt 2 = 0$$ or $$x + 5y + 5\sqrt 2 = 0$$
3

IIT-JEE 1979

Subjective
(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 $$4x - 3y + 2 = 0$$.

Answer

(a) $$(-4, -7)$$
(b) $$\left( {4 - \sqrt 5 } \right)x + \left( {2\sqrt 5 - 3} \right)y - \left( {4\sqrt 5 - 2} \right) = 0$$
4

IIT-JEE 1978

Subjective
One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertices are $$(-3, 1)$$ and $$(1, 1).$$ Find the equations of the other three sides.

Answer

$$\matrix{ {4x + 7y - 11 = 0} \cr {7x - 4y - 3 = 0} \cr {7x - 4y + 25 = 0} \cr } $$

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