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1

### 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.
2

### 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 $$3x + y + 7 = 0$$
3

### 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.
4

### IIT-JEE 1983

Subjective
The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, and $$P$$ is any point $$(x, y)$$. Show that the ratio of the area of the triangles $$\Delta$$ $$PBC$$ and $$\Delta$$$$ABC$$ is $$\left| {{{x + y - 2} \over 7}} \right|$$

Solve it.

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