The circle `x^2+y^2+2lambdax=0,lambda in R ,` touches the parabola `y^2=4x` externally. Then, (a)`lambda>0` (b) `lambda<0` (c)`lambda>1` (d) none of these

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

If the sum of the slopes of the normal from a point P to the hyperbola x y=c^2 is equal to lambda(lambda in R^+) , then the locus of point P is (a) x^2=lambdac^2 (b) y^2=lambdac^2 (c) x y=lambdac^2 (d) none of these

If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is 12 (b) -12 (c) 24 (d) -24

If y=2 is the directrix and (0,1) is the vertex of the parabola x^2+lambday+mu=0 , then (a) lambda=4 (b) mu=8 (c) lambda=-8 (d) mu=4

The number of integral values of lambda for which the equation x^2+y^2+lambdax+(1-lambda)y+5=0 is the equation fo a circle whose radius cannot exceed 5, is 14 (b) 18 (c) 16 (d) none of these

Portion of asymptote of hyperbola x^2/a^2-y^2/b^2 = 1 (between centre and the tangent at vertex) in the first quadrant is cut by the line y + lambda(x-a)=0 (lambda is a parameter) then (A) lambda in R (B) lambda in (0,oo) (C) lambda in (-oo,0) (D) lambda in R-{0}

The line x - b +lambda y = 0 cuts the parabola y^(2) = 4ax (a gt 0) at P(t_(1)) and Q(t_(2)) . If b in [2a, 4a] then range of t_(1)t_(2) where lambda in R is

The circles x^2+y^2-12 x-12 y=0 and x^2+y^2+6x+6y=0. touch each other externally touch each other internally intersect at two points none of these

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

Suppose the circle having equation x^2+y^2=3 intersects the rectangular hyperbola x y=1 at points A ,B ,C ,a n dDdot The equation x^2+y^2-3+lambda(x y-1)=0,lambda in R , represents. (a)a pair of lines through the origin for lambda=-3 (b)an ellipse through A ,B ,C ,a n dD for lambda=-3 (c)a parabola through A , B , C ,a n dD for lambda=-3 (d)a circle for any lambda in R