A normal is drawn to the hyperbolas `(y-x m)(m y+x)=a^2` and `(m^2-1)(y^2-x^2)+4m x y=b^2dot`find the angle between the hyperbolas.

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.

Let m_(1)" and " m_(2) be slopes of tengents from a point (1, 4) on the hyperbola x^(2)/(25) - y^(2)/ (16) = 1 . Find the point from which the tengents drawn on the hyperbola have slopes |m_(1)|" and "|m_(2)| and positive intercepts on y-axis.

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 is

Find the latus-rectum of the hyperbola x^2−4y^2=4

A normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 meets the axes at Ma n dN and lines M P and N P are drawn perpendicular to the axes meeting at Pdot Prove that the locus of P is the hyperbola a^2x^2-b^2y^2=(a^2+b^2)dot

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)

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 , is ((-a^2l)/n ,(b^2m)/n) (b) ((-a^2l)/m ,(b^2n)/m) ((a^2l)/m ,(-b^2n)/m) (d) ((a^2l)/m ,(b^2n)/m)

If equation of hyperbola is 4(2y -x -3)^(2) -9(2x + y - 1)^(2) = 80 , then

If the tangents drawn from a point on the hyperbola x^(2)-y^(2)=a^(2)-b^(2) to ellipse (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angle alpha and beta with the transverse axis of the hyperbola, then

If the distance between two parallel tangents having slope m drawn to the hyperbola (x^2)/9-(y^2)/(49)=1 is 2, then the value of 2|m| is_____