XI_ coordinate geometry Online Test

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
The centre of circle inscribed in square formed by the lines x2 -8x +12=0 and y2 -14y +45 =0, is
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
x1x2x3x4 = c4
y1y2y3y4= c4
All of above
The HR manager has expressed his interest in forming a quality circle, a voluntary group of staff from the Stores Department. This group would meet regularly to ________, ________ and _________ work related issues.
Identifying, solving, analyzing
Identify, solve, analyze
Identify, analyze, solve
Identifying, analyzing, solving
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}
Two circles x2 + y2 =6 and x2 +y2- 6x +8=0 are given. Then the equation of the circle through their points of intersection and the points (1,1) is
x2 +y2- 6x +4=0
x2 +y2- 3x +1=0
x2 +y2- 4y +2=0
None of these
The equation of the circle passing through (1,1) and the points of intersection of x2 + y2 + 13x –3y =0 and 2x2 + 2y2 + 4x –7y –25 =0 is
4x2 + 4y2 –30x – 10y –25 =0
4x2 + 4y2 +30x – 13y –25 =0
4x2 + 4y2 –17x – 10y +25 =0
None of these
The locus of the mid-point of chord of the circle x2 + y2 =4 which subtends a right angle at the origin is
x2 + y2 =2
x2 + y2 =1
x2 + y2 =2
x + y =1
If a circle passes through the point (a,b) and cuts the circle x2 + y2 =k2 orthogonally, then the equation of the locus of its centre is
2ax + 2by –(a2 + b2 + k2) =0
2ax + 2by –(a2 - b2 + k2) =0
x2 + y2 -3ax – 4by +(a2 - b2 + k2) =0
x2 + y2 –2ax –3by +(a2 - b2 + k2) =0


Nice questions, but can you discuss the solution methods?

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