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

The equation of the line AB is y = x . If A and B lie on the same side of the line mirror 2x-y = 1 , then the equation of the image of AB is (a) x+y-2=0 (b) 8x+y-9=0 (c) 7x-y-6=0 (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

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 equation of conjugate axis of the hyperbola x y-3y-4x+7=0 is (a) y+x=3 (b) y+x=7 (c) y-x=3 (d) none of these

Find the asymptotes of the curve x y-3y-2x=0 .

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

The equation of a hyperbola whose asymptotes are 3x +- 5y =0 and vertices are (+-5,0) is

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

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 x^2-y^2-5/2x y+5=0 2x^2-2y^2+5x y+5=0 2x^2+2y^2+5x y+10=0 none of these

For hyperbola whose center is at (1, 2) and the asymptotes are parallel to lines 2x+3y=0 and x+2y=1 , the equation of the hyperbola passing through (2, 4) is (a) (2x+3y-5)(x+2y-8)=40 (b) (2x+3y-8)(x+2y-5)=40 (c) (2x+3y-8)(x+2y-5)=30 (d) none of these