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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.

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.
 

Grade:12

1 Answers

Arun
25750 Points
4 years ago
Dear student
 
x - 2y  +4a = 0
 
y = ½ x + 2a
 
Now c = 2a
Also a/m = a/(1/2) = 2a
 
Since c = a/m
Hence line is a tangent
 
 

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