Let $$a_{1}, a_{2}, a_{3}, \ldots$$ be an arithmetic progression with $$a_{1}=7$$ and common difference 8. Let $$T_{1}, T_{2}, T_{3}, \ldots$$ be such that $$T_{1}=3$$ and $$T_{n+1}-T_{n}=a_{n}$$ for $$n \geq 1$$. Then, which of the following is/are TRUE ?

Consider the parabola $$y^{2}=4 x$$. Let $$S$$ be the focus of the parabola. A pair of tangents drawn to the parabola from the point $$P=(-2,1)$$ meet the parabola at $$P_{1}$$ and $$P_{2}$$. Let $$Q_{1}$$ and $$Q_{2}$$ be points on the lines $$S P_{1}$$ and $$S P_{2}$$ respectively such that $$P Q_{1}$$ is perpendicular to $$S P_{1}$$ and $$P Q_{2}$$ is perpendicular to $$S P_{2}$$. Then, which of the following is/are TRUE?