The auxiliary equation of circle of hyperbola `(x ^(2))/(a ^(2)) - (y^(2))/(b ^(2)) =1,` is

Equation of conjugate hyperbola w.r.t (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is

The equation of auxiliary circle of the hyperbola (x^(2))/(4)-(y^(2))/(9)=1 is

The parametric equations of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 are-

Find the equations of the tangents to the hyperbola (x ^(2))/(a ^(2)) - (y ^(2))/( b ^(2)) = 1 are mutually perpendicular, show that the locus of P is the circle x ^(2) + y ^(2) =a ^(2) -b ^(2).

The eqation of auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 is _

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

Equation auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (a

STATEMENT-1 : The line y = (b)/(a)x will not meet the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1, (a gt b gt 0) . and STATEMENT-2 : The line y = (b)/(a)x is an asymptote to the hyperbola.