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

The combined equation of the asymptotes of the hyperbola 2x^2 + 5xy + 2y^2 + 4x + 5y = 0 is -

The axis of the parabola x^(2)+2xy+y^(2)-5x+5y-5=0 is

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

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

Find the locus of the midpoints of chords of hyperbola 3x^(2)-2y^(2)+4x-6y=0 parallel to y = 2x.

The equation of a tangent to the hyperbola x^(2)-2y^(2)=2 parallel to the line 2x-2y+5=0 is-

Find the equation to the common chord of the two circles x^(2) + y^(2) - 4x + 6y - 36 = 0 and x^(2) + y^(2) - 5x + 8y - 43 = 0 .

The locus of the image of the point (2,3) in the line (x-2y+3)+lambda(2x-3y+4)=0 is (lambda in R) (a) x^2+y^2-3x-4y-4=0 (b) 2x^2+3y^2+2x+4y-7=0 (c) x^2+y^2-2x-4y+4=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-5)=40 (c) (2x+3y-8)(x+2y-5)=30 (d) none of these

Find the area of the figure enclosed by the curve 5x^2+6x y+2y^2+7x+6y+6=0.