1
IIT-JEE 2009 Paper 1 Offline
+3
-1
Tangents drawn from the point P (1, 8) to the circle
$${x^2}\, + \,{y^2}\, - \,6x\, - 4y\, - 11 = 0$$
touch the circle at the points A and B. The equation of the cirumcircle of the triangle PAB is
A
$${x^2}\, + \,{y^2}\, + \,4x\,\, - 6y\, + 19 = 0$$
B
$${x^2}\, + \,{y^2}\, - \,4x\,\, - 10y\, + 19 = 0$$
C
$${x^2}\, + \,{y^2}\, - \,2x\,\, + 6y\, - 29 = 0$$
D
$${x^2}\, + \,{y^2}\, - \,6x\,\, - 4y\, + 19 = 0$$
2
IIT-JEE 2008 Paper 2 Offline
+3
-1
Consider

$$\,{L_1}:\,\,2x\,\, + \,\,3y\, + \,p\,\, - \,\,3 = 0$$

$$\,{L_2}:\,\,2x\,\, + \,\,3y\, + \,p\,\, + \,\,3 = 0$$

where p is a real number, and $$\,C:\,{x^2}\, + \,{y^2}\, + \,6x\, - 10y\, + \,30 = 0$$

STATEMENT-1 : If line $${L_1}$$ is a chord of circle C, then line $${L_2}$$ is not always a diameter of circle C
and

STATEMENT-2 : If line $${L_1}$$ is a diameter of circle C, then line $${L_2}$$ is not a chord of circle C.

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct rexplanation for Statement-1
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct rexplanation for Statement-1
C
Statement-1 is True, Statement-2 is False
D
Statement-1 is False, Statement-2 is True
3
IIT-JEE 2008 Paper 1 Offline
+3
-1
A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $$\sqrt 3 x\, + \,y\, - \,6 = 0$$ and the point D is $$\left( {{{3\,\sqrt 3 } \over 2},\,{3 \over 2}} \right)$$. Further, it is given that the origin and the centre of C are on the same side of the line PQ.

The equation of circle C is

A
$${\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1$$
B
$${\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y + {1 \over 2})^2} = 1$$
C
$${\left( {x\, - \sqrt 3 \,} \right)^2} + {(y + 1)^2} = 1$$
D
$${\left( {x\, - \sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1$$
4
IIT-JEE 2008 Paper 1 Offline
+3
-1
A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $$\sqrt 3 x\, + \,y\, - \,6 = 0$$ and the point D is $$\left( {{{3\,\sqrt 3 } \over 2},\,{3 \over 2}} \right)$$. Further, it is given that the origin and the centre of C are on the same side of the line PQ.

Points E and F are given by

A
$$\left( {{{\,\sqrt 3 } \over 2},\,{3 \over 2}} \right),\,\left( {\sqrt 3 ,\,0} \right)$$
B
$$\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right),\,\left( {\sqrt 3 ,\,0} \right)$$
C
$$\left( {{{\,\sqrt 3 } \over 2},\,{3 \over 2}} \right),\,\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right)$$
D
$$\left( {{{\,3} \over 2},\,{{\sqrt 3 } \over 2}} \right),\,\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right)$$
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