Area of the quadrilateral formed with the foci of the hyperbola `x^2/a^2-y^2/b^2=1 and x^2/a^2-y^2/b^2=-1` (a) `4(a^2+b^2)` (b) `2(a^2+b^2)` (c) `(a^2+b^2)` (d) `1/2(a^2+b^2)`

Length of common tangents to the hyperbolas (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (y^(2))/(a^(2))-(x^(2))/(b^(2))=1 is

Show that the area of the quadrilateral formed by the common tangents to the circle x^(2)+y^(2)=c^(2) an the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1,b

The radius of the director circle of the hyperbola (x^(2))/(a(a+4b))-(y^(2))/(b(2a-b))=12a>b>0 is

The product of the perpendicular from two foci on any tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (A)a^(2)(B)((b)/(a))^(2)(C)((a)/(b))^(2) (D) b^(2)

The circle drawn on the line segment joining the foci of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 as diameter cuts the asymptotes at (A) (a,a) (b) (b,a)(C)(+-b,+-a)(D)(+-a,+-b)

For the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 and (x^(2))/(b^(2))+(y^(2))/(a^(2)) =1