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

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-8)=40 (c) (2x+3y-8)(x+2y-5)=30 (d) none of these

The combined equation of the asymptotes of the hyperbola 2x^2+5x y+2y^2+4x+5y=0 is (a) 2x^2+5x y+2y^2+4x+5y+2=0 (b) 2x^2+5x y+2y^2+4x+5y-2=0 (c) 2x^2+5x y+2y^2=0 (d) none of these

Equation of the circle through origin which cuts intercepts of length a\ a n d\ b on axes is a. x^2+y^2=a x+b y=0 b. x^2+y^2-a x-b y=0 c. x^2+y^2+b x+a y=0 d. 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 (2x+3y-5)(x+2y-8)=40 (2x+3y-8)(x+2y-8)=40 (2x+3y-8)(x+2y-5)=30 none of these

Equation of one of the tangents passing through (2, 8) to the hyperbola 5x^(2)-y^(2)=5 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 6x+3y-4c=0 (b) 3x+6y-5c=0 3x-6y-c=0 (d) none of these

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 6x+3y-4c=0 (b) 3x+6y-5c=0 3x-6y-c=0 (d) none of these

The equation of diameter of a circle passing through origin is x+y=1 and the greatest distance of any point of the circle from the diameter is sqrt(5) , then an equation of the circle is: (A) x^2+y^2-2x+4y=0 (B) x^2+y^2-4x+2y=0 (C) x^2+y^2+2x-2y=0 (D) none of these

The asymptotes of a hyperbola are parallel to lines 2x+3y=0 and 3x+2y=0 . The hyperbola has its centre at (1, 2) and it passes through (5, 3). Find its equation.

Equation of the hyperbola whose vertices are (+-3,0) and foci at (+-5,0) is a. 16 x^2-9y^2=144 b. 9x^2-16 y^2=144 c. 25 x^2-9y^2=225 d. 9x^2-25 y^2=81