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=3` (c)`x+y=2` (d) none of these

Find the equation of the circle which touch the line 2x-y=1 at (1,1) and line 2x+y=4

The equation of the bisector of the acute angle between the lines 2x-y+4=0 and x-2y=1 is (a) x-y+5=0 (b) x-y+1=0 (c) x-y=5 (d) none of these

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

A B C is a variable triangle such that A is (1,2) and B and C lie on line y=x+lambda (where lambda is a variable). Then the locus of the orthocentre of triangle A B C is (a) (x-1)^2+y^2=4 (b) x+y=3 (c) 2x-y=0 (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 x+y=2 (b) x-y=2 2x-y=1 (d) none of these

Two circle x^2+y^2=6 and x^2+y^2-6x+8=0 are given. Then the equation of the circle through their points of intersection and the point (1, 1) is (a) x^2+y^2-6x+4=0 (b) x^2+y^2-3x+1=0 (c) x^2+y^2-4y+2=0 (d)none of these

The locus fo the center of the circles 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

The locus of the point (h,k) for which the line hx+ky=1 touches the circle x^2+y^2=4

The center of a rectangular hyperbola lies on the line y=2xdot If one of the asymptotes is x+y+c=0 , then the other asymptote is (a) 6x+3y-4c=0 (b) 3x+6y-5c=0 (c) 3x-3y-c=0 (d) none of these

A circle touching the line x +y - 2 = 0 at (1,1) and cuts the circle x^(2) +y^(2) +4x +5y - 6 = 0 at P and Q. Then