\( T P \) and \( T Q \) are tangents to the parabola \( y^{2}=4 a x \) and the normals at \( P \...

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\( T P \) and \( T Q \) are tangents to the parabola \( y^{2}=4 a x \) and the normals at \( P \) and \( Q \) meet at a point \( R \) on the curve; prove that the centre of the circle circumscribing the triangle \( T P Q \) lies on the parabola \( 2 y^{2}=a(x-a) \).
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