(x^(2))/(a^(2))+(y^(2))/(b^(2))=1

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

The asymptotes of the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b_(1)^(2))=1 and (x^(2))/(a_(2)^(2))-(y^(2))/(b_(2)^(2))=1 are perpendicular to each other. Then,

The asymptotes of the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b_(1)^(2))=1 and (x^(2))/(a_(2)^(2))-(y^(2))/(b_(2)^(2))=1 are perpendicular to each other. Then,

Statement 1: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 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