If `a x+b y=1` is tangent to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` , then `a^2-b^2` is equal to (A) `1/(a^2e^2)` (B) `a^2e^2` (C) `b^2e^2` (D) none of these

If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then a^2-b^2 is equal to 1/(a^2e^2) (b) a^2e^2 b^2e^2 (d) none of these

If ax+by=1 is tangent to the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b^(2))=1, then a^(2)-b^(2) is equal to (A)(1)/(a^(2)e^(2))(B)a^(2)e^(2)(C)b^(2)e^(2)(D) none of these

If e is the eccentricity of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 , then e =

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

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

A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on the positive x- and y-axis. If this normal touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then a^2+b^2 is equal to (a) 5 (b) 25 (c) 16 (d) none of these

A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on the positive x- and y-axis. If this normal touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then a^2+b^2 is equal to (a)5 (b) 25 (c) 16 (d) none of these

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

If e_1 is the eccentricity of the hyperbola (y^(2))/(b^(2)) - (x^(2))/(a^(2)) = 1 then e_(1) =

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