Write the equation of the asymptotes of the hyperbola `(x^2)/(a^2) - (y^2)/(b^2) = 1`.

Find the equations to the common tangents to the two hyperbolas (x^2)/(a^2)-(y^2)/(b^2)=1 and (y^2)/(a^2)-(x^2)/(b^2)=1

Find the angle between the asymptotes of the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 .

Find the equations of the tangent and normal to the hyperbola x^2/a^2 - y^2/b^2 = 1 at the point (x_0,y_0)

If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is 120^0 and the product of perpendiculars drawn from the foci upon its any tangent is 9, then the locus of the point of intersection of perpendicular tangents of the hyperbola can be x^2+y^2=6 (b) x^2+y^2=9 x^2+y^2=3 (d) x^2+y^2=18

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

Find the equation of the tangent to the curve (X^2)/(a^2) + (y^2)/(b^2) = 1 at (x_0.y_0)

Find the area of the triangle formed by any tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 with its asymptotes.

The locus of the poles of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which subtend a right angle at its centre is