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 `

Show that the equation of the chord of the parabola x^(2) = 4ay joining the points (x_(1),y_(1)) ann (x_(2),y_(2)) on it is (x-x_(1))(x-x_(2))=x^(2)-4ay .

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 its (y-y_1)(y-y_2)=y^2-4ax.

The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-

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

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 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 .

Show that the equation of the straight line joining the points (x_(1),y_(1))and(x_(2),y_(2)) can be expressed in the form (x-x_(2))(y-y_(1))=(x-x_(1))(y-y_(2)) .

The point of intersection of the tangents to the parabola y^(2)=4ax at the points t_(1) and t_(2) is -

The point (8,4) lies inside the parabola y^(2) = 4ax If _

The length of the common chord of the parabolas y^(2)=x and x^(2)=y is