If the line `y=ax+1/2a-2` intersects the hyperbola `xy=1` at right angle in atleast one point then the possible integral value of `1/a` is

If the parabola y^(2)=4ax,a>0 cuts the hyperbola xy=sqrt(2) at right angles,then a=

STATEMENT-1 : The line 3x + 4y = 5 intersects the hyperbola 9x^(2) - 16y^(2) = 144 only at one point. and STATEMENT-2 : Given line is parallel to an asymptotes of the hyperbola.

STATEMENT-1 : The line 3x + 4y = 5 intersects the hyperbola 9x^(2) - 16y^(2) = 144 only at one point. and STATEMENT-2 : Given line is parallel to an asymptotes of the hyperbola.

A variable straight line with slope 2 intersects the hyperbola xy=1 at two pooints.Find the locus of the mid points of the line segment.

If the pair of lines joining the origin and the points of intersection of the line ax+by=1 and the curve x^(2)+y^(2)-x-y-1=0 are at right angles, then the locus of the point (a, b) is a circle of radius=

The lines x + y =|a| and ax-y= 1 intersect each other in the first quadrant. Then the set of all possible values of a is the interval.

The lines x + y=|a| and ax-y = 1 intersect each other in the first quadrant. Then the set of all possible values of a is the interval:

If the circles x ^(2) + y ^(2) + 5x -6y-1=0 and x ^(2) + y^(2) +ax -y +1=0 intersect orthogonally (the tangents at the point of intersection of the circles are at right angles), the value of a is

The lines joining the origin to the point of intersection of The lines joining the origin to the point of intersection of 3x^2+m x y=4x+1=0 and 2x+y-1=0 are at right angles. Then which of the following is not a possible value of m ? -4 (b) 4 (c) 7 (d) 3