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1

### IIT-JEE 2012 Paper 2 Offline

A tangent PT is drawn to the circle $${x^2}\, + {y^2} = 4$$ at the point P $$\left( {\sqrt 3 ,1} \right)$$. A straight line L, perpendicular to PT is a tangent to the circle $${(x - 3)^2}$$ + $${y^2}$$ = 1

A common tangent of the two circles is

A
x = 4
B
y = 2
C
$${x + \sqrt 3 \,y = 4}$$
D
$${x +2 \sqrt 2 \,y = 6}$$
2

### IIT-JEE 2012 Paper 2 Offline

A tangent PT is drawn to the circle $${x^2}\, + {y^2} = 4$$ at the point P $$\left( {\sqrt 3 ,1} \right)$$. A straight line L, perpendicular to PT is a tangent to the circle $${(x - 3)^2}$$ + $${y^2}$$ = 1.

A possible equation of L is

A
$${x - \sqrt 3 \,y = 1}$$
B
$${x + \sqrt 3 \,y = 1}$$
C
$${x - \sqrt 3 \,y = -1}$$
D
$${x + \sqrt 3 \,y = 5}$$
3

### IIT-JEE 2012 Paper 1 Offline

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle $${x^2}\, + \,{y^2} = 9$$ is
A
$$20\,({x^2}\, + \,{y^2}) - \,\,36x\,\, + \,\,45y = 0$$
B
$$20\,({x^2}\, + \,{y^2}) + \,\,36x\,\, - \,\,45y = 0$$
C
$$36\,({x^2}\, + \,{y^2}) - \,\,20x\,\, + \,\,45y = 0$$
D
$$36\,({x^2}\, + \,{y^2}) + \,\,20x\,\, - \,\,45y = 0$$
4

### IIT-JEE 2011 Paper 2 Offline

The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point.
A
$$\left( { - {3 \over 0},0} \right)$$
B
$$\left( { - {5 \over 2},2} \right)$$
C
$$\left( { - {3 \over 0},\,{5 \over 2}} \right)$$
D
(- 4, 0)

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