1
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
$${y^2} - 10x - 6y + 14 = 0$$
2
IIT-JEE 1993
Fill in the Blanks
+2
-0
If $$K = \sin \left( {\pi /18} \right)\sin \left( {5\pi /18} \right)\sin \left( {7\pi /18} \right),$$ then the numerical value of K is ______.
3
IIT-JEE 1993
Subjective
+5
-0
Consider a family of circles passing through two fixed points A (3, 7) and B (6, 5). Show that the chords on which the circle $${x^2}\, + \,{y^2} - \,4x - \,6y - 3 = 0$$ cuts the members of the family are concurrent at a point. Find the coordinate of this point.
4
IIT-JEE 1993
Fill in the Blanks
+2
-0
If in a triangle $$ABC$$, $${{2\cos A} \over a} + {{\cos B} \over b} + {{2\cos C} \over c} = {a \over {bc}} + {b \over {ca}},$$ then the value of the angle $$A$$ is .................... degrees.
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