Can we find where the normal is parallel to $y=x$?

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A curve has parametric equations \(x=5a\sec\theta,\,y=3a\tan\theta\), where \(-\frac{1}{2}\pi < \theta < \frac{1}{2}\pi\) and \(a\) is a positive constant. Find the coordinates of the point on the curve at which the normal is parallel to the line \(y=x\).