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The normals at P, Q, R on the parabola y...

The normals at P, Q, R on the parabola `y^2 = 4ax` meet in a point on the line `y = c.` Prove that the sides of the triangle PQR touch the parabola `x^2 = 2cy.`

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Normals at points P, Q and R of the parabola y^(2)=4ax meet in a point. Find the equation of line on which centroid of the triangle PQR lies.

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