Prove that the locus of intersections of tangents to the parabola \( y^{2}=4 a x \) which interc...

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Prove that the locus of intersections of tangents to the parabola \( y^{2}=4 a x \) which intercept a fixed length \( d \) on the directrix is \( \left(y^{2}-4 a x\right)(x+a)^{2}=d^{2} x^{2} \).
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