The locus of the center of the circle touching the line `2x-y=1` at `(1,1)` is (a)`x+3y=2` (b) `x+2y=2` (c)`x+y=2` (d) none of these

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is (a) x+y=2 (b) x-y=2 (c) 2x-y=1 (d) none of these

The locus of the center of the circle such that the point (2,3) is the midpoint of the chord 5x+2y=16 is (a) 2x-5y+11=0 (b) 2x+5y-11=0 (c) 2x+5y+11=0 (d) none of these

Find the locus of the center of the circle touching the circle x^2+y^2-4y-2x=4 internally and tangents on which from (1, 2) are making of 60^0 with each other.

A line from (-1,0) intersects the parabola x^(2)= 4y at A and B. Then the locus of centroid of DeltaOAB is (where O is origin) (a) 3x^(2) -2x =4y (b) 3y^(2) -2y = 4x (c) 3x^(2) +2x=4y (d) none of these

The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (a) (-1/2,1/2) (b) (1, 1) (c) (1/2,1/2) (d) none of these

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 (c) y^2-x^2=((27)/7)^2 (d) none of these

The slopes of the common tangents of the ellipse (x^2)/4+(y^2)/1=1 and the circle x^2+y^2=3 are +-1 (b) +-sqrt(2) (c) +-sqrt(3) (d) none of these

The locus of the midpoint of a chord of the circle x^2+y^2=4 which subtends a right angle at the origins is (a) x+y=2 (b) x^2+y^2=1 x^2+y^2=2 (d) x+y=1

The radius of the circle touching the parabola y^2=x at (1, 1) and having the directrix of y^2=x as its normal is

Tangents P A and P B are drawn to x^2+y^2=9 from any arbitrary point P on the line x+y=25 . The locus of the midpoint of chord A B is (a) 25(x^2+y^2)=9(x+y) (b) 25(x^2+y^2)=3(x+y) (c) 5(x^2+y^2)=3(x+y) (d) none of these