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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.
Dear student x - 2y +4a = 0 y = ½ x + 2a Now c = 2aAlso a/m = a/(1/2) = 2a Since c = a/mHence line is a tangent
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