Find the shortest distance from the parabola
$$y^2=64x \tag{1}$$ to the straight-line
$$4x+3y+46=0\tag{2}$$ I guess, to first find
$$x=-\frac{3y+46}{4}\tag{3}$$
and than substitue it into the parabola equation, but this way take to much time, moreover i`m not sure that its right, any hints are welcome
[Math] The shortest distance from the parabola to the straight-line
conic sections
Best Answer
Hint: Two possible ways to resolve: as an extremal problem, finding minimal value; or geometric approach, as a distance between two parallels where one is a tangent of parabola