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 `(2asqrt2,0).` Then the eccentricity of the hyperbola 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 2 (b) sqrt(2) (c) 3 (d) sqrt(3)

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)).

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

The tangents and normal at a point on (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 cut the y-axis A and B. Then the circle on AB as diameter passes through

The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1 . If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

The number of normals to the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 from an external point is _______

The circle passing through the point (-1,0) and touching the y-axis at (0,2) also passes through the point:

The tangents drawn from a point P to ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 make angles alpha and beta with the transverse axis of the hyperbola, then

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.