Show that the tangent at one extremity of a focal chord of a parabola is parallel to the normal at the other extremity.
Let be the two extremeties of a focal chord
of the given parabola.
Equation of the tangent at P is . equation 2
Slope of this equation is .
Equation of the normal at Q is
Slope of the normal is which is the slope of
the equation 2.
Therefore tangent at P is parallel to the normal at Q.