Show that the lines joining the origin to the point of intersection of the line Show that the lines joining the origin to the point of intersection of the line $x+y=1$ with the curve $4x^2+4y^2+4x-2y-5=0$ are at right angles to each other. 
How do I approach this? Please help.

Solving of the system gives 
$$4x^2+4(1-x)^2+4x-2(1-x)-5=0$$ or
$$8x^2-2x-3=0,$$ which gives the following points: $\left(\frac{3}{4},\frac{1}{4}\right)$ and $\left(-\frac{1}{2},\frac{3}{2}\right)$.
Now, $$m_1=\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{1}{3}$$ and
$$m_2=\frac{\frac{3}{2}}{-\frac{1}{2}}=-3$$ and since $m_1m_2=-1$, we are done!
