Grade 12Vectors
Prove that the line x − 2y + 4a = 0 touches the parabola y2 = 4ax, and find the
coordinates of P, the point of contact. If the line x−2y +2a = 0 meets the parabola
in Q, R, and M is the mid-point of QR, prove that PM is parallel to the axis of x,
and that this axis and the line through M perpendicular to it meet on the normal at
P to the parabola.
Prove that the line x − 2y + 4a = 0 touches the parabola y2 = 4ax, and find the
coordinates of P, the point of contact. If the line x−2y +2a = 0 meets the parabola
in Q, R, and M is the mid-point of QR, prove that PM is parallel to the axis of x,
and that this axis and the line through M perpendicular to it meet on the normal at
P to the parabola.
coordinates of P, the point of contact. If the line x−2y +2a = 0 meets the parabola
in Q, R, and M is the mid-point of QR, prove that PM is parallel to the axis of x,
and that this axis and the line through M perpendicular to it meet on the normal at
P to the parabola.
