Let `P(6, 3)` be a point on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1.` If the normal at point P intersects the x-axis at (9, 0), then find the eccentricity of the hyperbola.

Let P(4,3) be a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If the normal at P intersects the x-axis at (16,0), then the eccentriclty of the hyperbola is

Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

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.

the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(25)=1 is

If e is the eccentricity of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 , then e =

The eccentricity of the hyperbola x^2-y^2=4 is

Let P(a sec theta , b tan theta ) and Q(a sec phi , b tan phi) where theta + phi = (pi)/(2) be two point on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1 .If ( h, k) be the point of intersection of the normals at P and Q , then the value of k is -

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

The slop of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( a sec theta , b tan theta) is -

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is