Question:

Consider the parabola $\mathbf{y^2 = 4x}$. Let $\mathbf{S}$ be the focus of the parabola. A pair of tangents drawn to the parabola from the point $\mathbf{P= (-2, 1)}$ meet the parabola at $\mathbf{P_1}$ and $\mathbf{P_2}$. Let $\mathbf{Q_1}$ and $\mathbf{Q_2}$ be points on the lines $\mathbf{SP_1}$ and $\mathbf{SP_2}$ respectively such that $\mathbf{PQ_1}$ is perpendicular to $\mathbf{SP_1}$ and $\mathbf{PQ_2}$ is perpendicular to $\mathbf{SP_2}$. Then, which of the following is/are TRUE?