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1

### IIT-JEE 1985

Subjective
Two sides of rhombus $$ABCD$$ are parallel to the lines $$y = x + 2$$ and $$y = 7x + 3$$. If the diagonals of the rhombus intersect at the point $$(1, 2)$$ and the vertex $$A$$ is on the $$y$$-axis, find possible co-ordinates of $$A$$.

$$(0 ; 0)$$ or $$\left( {0,\,{\raise0.5ex\hbox{5} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{2}}} \right)$$
2

### IIT-JEE 1985

Subjective
One of the diameters of the circle circumscribing the rectangle $$ABCD$$ is $$4y = x + 7$$. If $$A$$ and $$B$$ are the points $$(-3, 4)$$ and $$(5, 4)$$ respectively, then find the area of rectangle.

32 sq. units.
3

### IIT-JEE 1984

Subjective
Two equal sides of an isosceles triangle are given by the equations $$7x - y + 3 = 0$$ and $$x + y - 3 = 0$$ and its thirds side passes through the point $$(1, -10)$$. Determine the equation of the third side.

$$x - 3y - 31 = 0$$ or $$3x + y + 7 = 0$$
4

### IIT-JEE 1983

Subjective
The end $$A, B$$ of a straight line segment of constant length $$c$$ slide upon the fixed rectangular axes $$OX, OY$$ respectively. If the rectangle $$OAPB$$ be completed, then show that the locus of the foot of the perpendicular drawn from $$P$$ to $$AB$$ is $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {c^{{2 \over 3}}}$$

Solve it.

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