1
IIT-JEE 2005
Subjective
+2
-0
The area of the triangle formed by intersection of a line parallel to $$x$$-axis and passing through $$P (h, k)$$ with the lines $$y = x$$ and $$x + y = 2$$ is $$4{h^2}$$. Find the locus of the point $$P$$.
2
IIT-JEE 2002
Subjective
+5
-0
A straight line $$L$$ through the origin meets the lines $$x + y = 1$$ and $$x + y = 3$$ at $$P$$ and $$Q$$ respectively. Through $$P$$ and $$Q$$ two straight lines $${L_1}$$ and $${L_2}$$ are drawn, parallel to $$2x - y = 5$$ and $$3x + y = 5$$ respectively. Lines $${L_1}$$ and $${L_2}$$ intersect at $$R$$. Show that the locus of $$R$$, as $$L$$ varies is a straight line.
3
IIT-JEE 2002
Subjective
+5
-0
A straight line $$L$$ with negative slope passes through the point $$(8, 2)$$ and cuts the positive coordinate axes at points $$P$$ and $$Q$$. Find the absolute minimum value of $$OP + OQ,$$ as $$L$$ varies, where $$O$$ is the origin.
4
IIT-JEE 2001
Subjective
+6
-0
Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that

the equation $$\left| {\matrix{ {ax - by - c} & {bx + ay} & {cx + a} \cr {bx + ay} & { - ax + by - c} & {cy + b} \cr {cx + a} & {cy + b} & { - ax - by + c} \cr } } \right| = 0$$

represents a straight line.
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