A line which makes an acute angle $\theta$ with the positive direction of $x$-axis is drawn through $P(3,4)$ to cut the curve $y^2=4x$ at $Q$ and $R$. Show that the lengths of the segments $PQ$ and $PR$ are numerical values of the roots of the equation $r^2\sin^2\theta+4r(2\sin\theta-\cos\theta)+4=0$.
Here is what I have done so far. Consider the parametric form of the line $x_{1}=3-r\cos\theta$ and $y_{1}=4-r\sin\theta$. I have affixed a $-$ sign to account for the fact that $(3,4)$ lies outside the parabola. Now all that is required is that $(x_{1},y_{1})$ lies on the parabola. Putting this into the equation of the parabola gives $r^2\sin^2\theta-4r(2\sin\theta-\cos\theta)+4=0$.
I am getting a $-$ sign in the required equation. Why is that? What if a point was inside the parabola, would we have affixed a $-$ sign to $r$ in writing the parametric form? Thanks.