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1

### IIT-JEE 1992

Subjective
Determine all values of $$\alpha$$ for which the point $$\left( {\alpha ,\,{\alpha ^2}} \right)$$ lies insides the triangle formed by the lines $$\matrix{ {2x + 3y - 1 = 0} \cr {x + 2y - 3 = 0} \cr {5x - 6y - 1 = 0} \cr }$$\$

$$\alpha \in \left( { - {3 \over 2}, - 1} \right) \cup \left( {{1 \over 2},1} \right)$$
2

### IIT-JEE 1991

Subjective
Find the equation of the line passing through the point $$(2, 3)$$ and making intercept of length 2 units between the lines $$y + 2x = 3$$ and $$y + 2x = 5$$.

$$3x + 4y - 18 = 0$$ or $$x - 2 = 0$$
3

### IIT-JEE 1991

Subjective
Show that all chords of the curve $$3{x^2} - {y^2} - 2x + 4y = 0,$$ which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.

$$(1, -2)$$
4

### IIT-JEE 1990

Subjective
A line cuts the $$x$$-axis at $$A (7, 0)$$ and the $$y$$-axis at $$B (0, -5)$$. A variable line $$PQ$$ is drawn perpendicular to $$AB$$ cutting the $$x$$axis in $$P$$ and they $$Y$$-axis in $$Q$$. If $$AQ$$ and $$BP$$ intersect at $$R$$, find the locus of R.

$${x^2} + {y^2} - 7x + 5y = 0$$

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Class 12