If the circle `x^2+y^2+2gx+2fy+c=0` is touched by `y=x` at `P` such that `O P=6sqrt(2),` then the value of `c` is (a)36 (b) 144 (c) 72 (d) none of these

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

If the length of the common chord of two circles x^2+y^2+8x+1=0 and x^2+y^2+2muy-1=0 is 2sqrt(6) , then the values of mu are (a) +-2 (b) +-3 (c) +-4 (d) none of these

If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane 2x-y+sqrt(pz)+4=0 is such that sintheta=1/3 , then the values of p is (A) 0 (B) 1/3 (C) 2/3 (D) none of these

If the circles x^2 + y^2 + 2ax + b = 0 and x^2+ y^2+ 2cx + b = 0 touch each other (a!=c)

The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the length P Q is equal to (A) 2 (B) 2sqrt(2) (C) 4 (D) none of these

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

There are two circles whose equation are x^2+y^2=9 and x^2+y^2-8x-6y+n^2=0,n in Zdot If the two circles have exactly two common tangents, then the number of possible values of n is 2 (b) 8 (c) 9 (d) none of these

If the pair of lines ax^(2) + 2hxy + by^(2)+ 2gx + 2fy + c = 0 intersect on the y-axis then

If the equation a x^2-6x y+y^2 +2gx +2fy +c=0 represents a pair of lines whose slopes are m and m^2, then the value(s) of a is/are

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