A line through $$A (-5, -4)$$ meets the line $$x + 3y + 2 = 0,$$ $$2x + y + 4 = 0$$ and $$x - y - 5 = 0$$ at the points $$B, C$$ and $$D$$ respectively. If $${\left( {15/AB} \right)^2} + {\left( {10/AC} \right)^2} = {\left( {6/AD} \right)^2},$$ find the equation of the line.
Answer
$$2x + 3y + 22 = 0$$
2
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
$$$\matrix{
{2x + 3y - 1 = 0} \cr
{x + 2y - 3 = 0} \cr
{5x - 6y - 1 = 0} \cr
} $$$
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 $$y + 2x = 5$$.
Answer
$$3x + 4y - 18 = 0$$ or $$x - 2 = 0$$
4
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.
Answer
$$(1, -2)$$
Questions Asked from Straight Lines and Pair of Straight Lines
On those following papers in Subjective
Number in Brackets after Paper Indicates No. of Questions
