Find the locus of the point of intersection of the tangents to the parabolas $y^2=4(x+1)$ and $y^2=8(x+2)$ which are at right angles.
Equation of tangents will be
$y=m_1(x+1)+1/m_1$ and $y=m_2(x+2)+2/m_2$
Now even if I use the condition that $m_1 \cdot m_2=-1$, I am not able to eliminate $m_1$. Please help me with this.