The centre of a rectangular hyperbola lies on the line y =2x. If one of the asymptotes is `x+y+c=0`, then the other asymptote is

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-6y-c=0 (d) none of these

If the foci of a hyperbola lie on y=x and one of the asymptotes is y=2x , then the equation of the hyperbola, given that it passes through (3, 4), is (a) x^2-y^2-5/2x y+5=0 (b) 2x^2-2y^2+5x y+5=0 (c) 2x^2+2y^2-5x y+10=0 (d) none of these

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

The chord of contact of a point P w.r.t a hyperbola and its auxiliary circle are at right angle. Then the point P lies (a) on conjugate hyperbola (b) one of the directrix (c) one of the asymptotes (d) none of these

The equation of a rectangular hyperbola whose asymptotes are x=3 and y=5 and passing through (7,8) is

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then

The equation of a tangent to the hyperbola 3x^(2)-y^(2)=3 , parallel to the line y = 2x +4 is

From a point P(1,2) , two tangents are drawn to a hyperbola H in which one tangent is drawn to each arm of the hyperbola. If the equations of the asymptotes of hyperbola H are sqrt(3)x-y+5=0 and sqrt(3)x+y-1=0 , then the eccentricity of H is 2 (b) 2/(sqrt(3)) (c) sqrt(2) (d) sqrt(3)

If one end of the diameter is (1, 1) and the other end lies on the line x+y=3 , then find the locus of the center of the circle.

Equation of the rectangular hyperbola whose focus is (1,-1) and the corresponding directrix is x-y+1=0 .