If from any point `P(x_(1),y_(1))` on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1,` then prove that corresponding chord of contact touches the another branch of the hyperbola `(x^(2))/(a^(2))-(y^(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.

Locus of perpendicular from center upon normal to the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 is

Prove that the length of the latusrection of the hyperbola x^(2)/a^(2) -y^(2)/b^(2) =1 " is" (2b^(2))/a

The eccentricity of the hyperbola (y^(2))/(9)-(x^(2))/(25)=1 is …………………

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0), y_(0)).

Find the area of the triangle formed by any tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 with its asymptotes.

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the axes in M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)

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