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 `(x1 2)/(a^2)-(y1 2)/(b^2)<1`

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

The point (at^(2),2bt) lies on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 for

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the vlaue of (1)/(y_(1))+(1)/(y_(2)) is

Find the area of the smaller region bounded by the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the line (x)/(a)+(y)/(b)=1

A point on the curve (x ^(2))/(A ^(2)) - (y^(2))/(B ^(2)) =1 is

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

The point (1,2) lies inside the circle x^(2)+y^(2)-2x+6y+1=0 .