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.

If cos ^(-1)\ (x)/(a) + cos^(-1)\ (y)/(b) = theta , then (x^(2))/(a^(2)) +(y^(2))/(b^(2))=?

If the polars of (x_1,y_1)" and "(x_2,y_2) with respect to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 are at the right angels, where (x_1x_2)b^4+a^4(y_1y_2)=lambda , then lambda the value of is

Find the condition for the following set of curves to intersect orthogonally: (x^2)/(a^2)-(y^2)/(b^2)=1 and x y=c^2 (x^2)/(a^2)+(y^2)/(b^2)=1 and (x^2)/(A^2)-(y^2)/(B^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 value of (1)/(y_(1))+(1)/(y_(2)) is

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

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

Find the area of the region {(x ,\ y):(x^2)/(a^2)+(y^2)/(b^2)lt=1<=x/a+y/b}

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

If the chords of contact of tangents from two points (x_(1),y_(1)) and (x_(2),y_(2)) to the elipse x^(2)/a^(2)+y^(2)/b^(2)=1 are at right angles, then find (x_(1)x_(2))/(y_(1)y_(2))