Parabola – JEE Main Previous Year Question with Solutions

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Let PQ be a focal chord of the parabolas $\mathrm{y}^{2}=4 \mathrm{ax} .$ The tangents to the parabola at $\mathrm{P}$ and $\mathrm{Q}$ meet at a point lying on the line $\mathrm{y}=2 \mathrm{x}+\mathrm{a}, \mathrm{a}>0 .$
Let a,r,s, t be nonzero real numbers. Let $P\left(a t^{2}, 2 a t\right), Q, R\left(a r^{2}, 2 a r\right)$ and $S\left(a s^{2}, 2 a s\right)$ be distinct points on the parabola $y^{2}=4 a x .$ Suppose that $P Q$ is the focal chord and lines $Q R$ and $P K$ are parallel, where $K$ is the point $(2 a, 0) .$
The value of $r$ is-