1
JEE Advanced 2019 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
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A line y = mx + 1 intersects the circle $${(x - 3)^2} + {(y + 2)^2}$$ = 25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate $$ - {3 \over 5}$$, then which one of the following options is correct?
A
6 $$ \le $$ m < 8
B
$$ - $$3 $$ \le $$ m < $$ - $$1
C
4 $$ \le $$ m < 6
D
2 $$ \le $$ m < 4
2
IIT-JEE 2012 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
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 2 Offline
MCQ (Single Correct Answer)
+4
-1
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
$${x +2 \sqrt 2 \,y = 6}$$
4
IIT-JEE 2012 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
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
$$36\,({x^2}\, + \,{y^2}) + \,\,20x\,\, - \,\,45y = 0$$
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