I have a parabola $(y+5)^2 = 4x$ and I need to find its minimum distance from origin. Scientific calculators aren't allowed. I have tried :
1) Substituting parametric coordinates $(r\cos Q, r\sin Q)$ but the expression of $r$ in $Q$ obtained after differenciation doesn't give roots which can be calculated by hand.
2) Used point form of tangent for $(x_1,y_1)$ on parabola and made line joining origin and $(x_1,y_1)$ perpendicular but it forms a cubic equation which again can't be solved by hand.
Help please!
The solution DO involves solving a cubic equation, which, by the way, CAN be solved by hand with Cardano's method.