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))` , prove that `t_(1)t_(2) = - 1 `

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

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:

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

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

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 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) .

If the normal at (at_(1)^(2), 2at_(1))" to " y^(2) =4ax intersect the parabola at (at_(2)^(2), 2at_(2)) , prove that, t_(1)+t_(2)+(2)/(t_1)=0(t_(1) ne 0)

If a straight line pasing through the focus of the parabola y^(2) = 4ax intersects the parabola at the points (x_(1), y_(1)) and (x_(2) , y_(2)) then prove that y_(1)y_(2)+4x_(1)x_(2)=0 .