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`

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 locus of the point which divides the double ordinates of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 in the ratio 1:2 internally is (x^2)/(a^2)+(9y^2)/(b^2)=1 (b) (x^2)/(a^2)+(9y^2)/(b^2)=1/9 (9x^2)/(a^2)+(9y^2)/(b^2)=1 (d) none of these

Find the area between the ellpise (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and lines (|x|)/(a)+(|y|)/(b)=1

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

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

If the chords of contact of tangents from two poinst (x_1, y_1) and (x_2, y_2) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are at right angles, then find the value of (x_1x_2)/(y_1y_2)dot