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

Show that the acute angle between the asymptotes of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a^2> b^2), is 2cos^(-1)(1/e), where e is the eccentricity of the hyperbola.

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 (a) x^2+y^2=6 (b) x^2+y^2=9 (c) x^2+y^2=3 (d) x^2+y^2=18

If the angle between the asymptotes of hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 id (pi)/(3) , then the eccentnricity of conjugate hyperbola is _________.

In each of the find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. (x^(2))/(16)-(y^(2))/(9)=1

How many real tangents can be drawn from the point (4, 3) to the hyperbola (x^2)/(16)-(y^2)/9=1? Find the equation of these tangents and the angle between them.

If tangents drawn from the point (a ,2) to the hyperbola (x^2)/(16)-(y^2)/9=1 are perpendicular, then the value of a^2 is _____

If the latus rectum subtends a right angle at the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then find its eccentricity.

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+9y^2+14 x+22 y+7=0

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+8y^2+14 x+22 y+7=0

Find the equation of pair of tangents drawn from point (4, 3) to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 . Also, find the angle between the tangents.