If the extremities of a focal chord of the parabola `y^(2) = 4ax ` be `(at_(1)^(2) , 2at_(1))` and `(at_(2)^(2) ,2at_(2))` , show that `t_(1)t_(2) = - 1 `

If the extremitied of a focal chord of the parabola y^2=4ax be (at_1^2,2at_1) and (at_2^2,2at_2) ,show that t_1t_2=-1

The distance between the points (at_1^(2) , 2at_(1)) and (at_(2)^(2) ,2at_(2)) is

Length of the shortest normal chord of the parabola y^2=4ax is

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

If alpha and beta be the eccentric angles of the extremities of a focal chord of the hyperbola b^(2)x^(2) - a^(2)y^(2) = a^(2)b^(2) , show that, tan(alpha)/(2)tan(beta)/(2) = -(e-1)/(e+1) , (e-1)/(e+1) (e is the eccentricity of the hyperbola.).

Show that the equation of the chord of the parabola y^(2) = 4ax through the points (x_(1),y_(1)) and (x_(2),y_(2)) on it is (y-y_(1))(y-y_(2)) = y^(2) - 4ax

If athe coordinates of one end of a focal chord of the parabola y^(2) = 4ax be (at^(2) ,2at) , show that the coordinates of the other end point are ((a)/(t^(2)),(2a)/(t)) and the length of the chord is a(t+(1)/(t))^(2)

If (at^(2) , 2at ) be the coordinates of an extremity of a focal chord of the parabola y^(2) = 4ax , then show that the length of the chord is a(t+(1)/(t))^(2) .

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

If a straight line passing through the focus of the parabola y^(2) = 4ax intersectts the parabola at the points (x_(1), y_(1)) and (x_(2), y_(2)) , then prove that x_(1)x_(2)=a^(2) .