Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by
The equation of normal is
y = mx $$-$$ 2m $$-$$ m3
As (9, 6) lies on it, 6 = 9m $$-$$ 2m $$-$$ m33 $$-$$ 7m + 6 = 0
The roots are m = 1, 2, $$-$$3. So the normal are
y = x $$-$$ 3, y = 2x $$-$$ 12, y = $$-$$3x + 33.