Equation of a line is given by $y + 2at = t( x - at^2)$, $t$ being a parameter. Find the locus of the point of intersection of the line which are at right angles?
My Approach: I found out the point of intersection ($a(\frac{t^4 + t^2 + 1}{t^2}), a(\frac{1-t^2}{t}))$.
Don't know how to proceed further.
You already got point of intersection as $$ a\left(\frac{t^4+t^2+1}{t^2}\right) , a\left(\frac{1-t^2}{t}\right) $$ So $$ y^2 =a^2\left(\frac{t^4-2t^2+1}{t^2}\right)$$ $$ y^2 +3a^2 = a^2\left(\frac{t^4+t^2+1}{t^2}\right)= ax$$
Therefore $y^2+3a^2=ax$ is the required locus