AIEEE,IIT JEE MATHS-CIRCLE Online Test

The angle between a pair of tangents drawn from a point P to the circle x2 +y2 +4x –6y +9 sin2 ( + 13 cos2 ( =0 is 2(. The equation of the locus of the point P is
x2 +y2 +4x –6y +4=0
x2 +y2 +4x –6y –9 =0
x2 +y2 +4x –6y –4 =0
x2 +y2 +4x –6y +9 =0
Let AB be a chord of the circle x2 +y2 =r2 subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as P moves on the circle is
a parabola
a circle
an ellipse
a pair of straight lines
If two distinct chords, drawn from the point (p, q) on the circle x2 + y2 =px +qy (where pq ( 0) are bisected by the x-axis, then
p2 =q2
p2 =8q2
p2 <8q2
p2 >8q2
The centre of circle inscribed in square formed by the lines x2 -8x +12=0 and y2 -14y +45 =0, is
(4,7)
(7,4
(9,4)
(4,9)
The equations of the tangents drawn from the origin to the circle x2 +y2 -2rx -2hy +h2=0, are
x =0
y =0
(h2 –r2)x -2hy =0
(h2 +r2)x +2hy =0
1 and 3
2 and 4
If the circle x2 +y2 =a2 intersects the hyperbola xy =c2 in four points P(x1, y1), Q(x2, y2), R(x3, y3), S(x4, y4), then
x1+x2+x3+x4=0
y1+y2+y3+y4=0
x1x2x3x4 = c4
y1y2y3y4= c4
All of above
A circle is given by x2 +(y-1)2 =1, another circle C touches it externally and also the x-axis, then the locus of its centre is
{(x, y): x2 =4y} ( {(x, y): y<0}
{(x, y): x2 +(y-1)2=4} ( {(x, y): y(0}
{(x, y): x2 =y} ( {(0, y): y(0}
{(x, y): x2 =4y} ( {(0, y): y(0}
The number of common tangents to the circle x2 +y2 =4 and x2 +y2 -6x -8y =24 is
0
1
3
4
The circles x2 +y2 -10x + 16=0 and x2 +y2 =r2 intersect each other in two distinct points if
r<2
r>8
2 2( r (8
The lines 2x –3y =5 and 3x –4y =7 are diameters of a circle of area 154 sq. Then the equation of this circle is
x2+ y2 +2x –2y =62
x2+ y2 +2x –2y =47
x2+ y2 -2x +2y =47
x2+ y2 -2x +2y =62
Discussion

Alisha

hey! how to do ques 5.. i got x=0 as tangent but not the other one and also ques 2 the hyperbola ques.
thanks.. :)

2807 days 1 hours 33 minutes ago

avinash trunk

got 9 right think so answer of ques 1 is d but its given b

3979 days 16 hours 53 minutes ago

saurabh

plase incres the Q.

4247 days 4 hours 34 minutes ago

saurabh

easy q.

4247 days 4 hours 35 minutes ago

Kajal Sengupta
Physics 9th to 12 th grade,CIE, Edexcel, AP, IB , CBSE, ICSE
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