The tangent at a point P on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` meets one of the directrix at F. If PF subtends an angle `theta` at the corresponding focus, then `theta` =

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 meets one of the directrix at Fdot If P F subtends an angle theta at the corresponding focus, then theta= pi/4 (b) pi/2 (c) (3pi)/4 (d) pi

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 tangent at the point theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , meets its auxiliary circle at two points whose join subtends a right angle at the centre, show that the eccentricity of the ellipse is given by, (1)/(e^(2))=1+sin^(2)theta

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x0, y0).

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 slop of the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 at the point (a cos theta, b sin 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

Find the equation of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at ( a sec, theta b tan theta) . Hence show that if the tangent intercepts unit length on each of the coordinate axis than the point (a,b) satisfies the equation x^(2)-y^(2)=1

Find the equation of tangent at the specified point on the following curve : (x^(2))/(a^(2))-(y^(2))/(b^(2))=1" at"( a sec theta, b tan theta)

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 -