1
IIT-JEE 1993
Subjective
+5
-0
Tagent at a point $${P_1}$$ {other than $$(0, 0)$$} on the curve $$y = {x^3}$$ meets the curve again at $${P_2}$$. The tangent at $${P_2}$$ meets the curve at $${P_3}$$, and so on. Show that the abscissae of $${P_1},\,{P_2},{P_3}......{P_n},$$ form a G.P. Also find the ratio.

[area $$\left( {\Delta {P_1},{P_2},{P_3}} \right)$$]/[area $$\left( {{P_2},{P_3},{P_4}} \right)$$]

2
IIT-JEE 1993
Subjective
+5
-0
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.
3
IIT-JEE 1993
Fill in the Blanks
+2
-0
The equation of the locus of the mid-points of the circle $$4{x^2} + 4{y^2} - 12x + 4y + 1 = 0$$ that subtend an angle of $$2\pi /3$$ at its centre is.................................
4
IIT-JEE 1993
MCQ (Single Correct Answer)
+1
-0.25
The locus of the centre of a circle, which touches externally the circle $${x^2} + {y^2} - 6x - 6y + 14 = 0$$ and also touches the y-axis, is given by the equation:
A
$${x^2} - 6x - 10y + 14 = 0$$
B
$${x^2} - 10x - 6y + 14 = 0$$
C
$${y^2} - 6x - 10y + 14 = 0$$
D
$${y^2} - 10x - 6y + 14 = 0$$
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