If `P(x_(1),y_(1))` is a point on the hyperbola `x^(2)-y^(2)=a^(2)`, then `SO.S'P=` . . . .

If P(x_(1),y_(1)) is a point on the hyperbola x^(2)-y^(2)=a^(2) , then SP.S'P= . . . .

If a point (x_(1),y_(1)) lies in the shaded region (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, shown in the figure,then (x^(2))/(a^(2))-(y^(2))/(b^(2))<0 statement 2: If P(x_(1),y_(1)) lies outside the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, then (x_(1)^(2))/(a^(2))-(y_(1)^(2))/(b^(2))<1

If P is a point on the rectangular hyperbola x^(2)-y^(2)=a^(2),C is its centre and S,S ,are the two foci,then the product (SP.S'P)=

If P is a point on the rectangular hyperbola x^(2)-y^(2)=a^(2),C is its centre and S,S ,are the two foci,then the product (SP.S'P)=

If P(theta) is a point on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 , whose foci are S and S', then SP.S'P =

Let P be a point on the hyperbola x^(2)-y^(2)=a^(2), where a is a parameter,such that P is nearest to the line y=2x. Find the locus of P.

Let P(4,3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the normal at P intersects the x-axis at (16,0), then the eccentricity of the hyperbola is

If P is a point on the hyperbola 16x^(2) - 9y^(2) = 144 whose foci are S_(1)" and " S_(2) " then : " | S_(1) P - S_(2) P | =

tangent is drawn at point P(x_(1),y_(1)) on the hyperbola (x^(2))/(4)-y^(2)=1. If pair of tangents are drawn from any point on this tangent to the circle x^(2)+y^(2)=16 such that chords of contact are concurrent at the point (x_(2),y_(2)) then