Question 1196491
 

let vertex be at origin, V({{{0}}},{{{0}}})

if the reflector is {{{30cm}}} wide and {{{15cm}}} deep, we have two points that lie on parabola and these are:

({{{15}}},{{{15}}}) and ({{{15}}},{{{-15}}}) (means parabola opens to the right)


general formula for this parabola is:

{{{y^2=4px}}}

The value of {{{p}}} is the {{{distance}}} from the {{{vertex}}} to the {{{focus}}} of the parabola. A focus always lies on the axis of its parabola.


use one point to calculate {{{p}}}

{{{15^2=4p*15}}}........simplify

{{{15=4p}}}

{{{p=15/4}}}

{{{p=3.75}}}

your parabola is:

{{{y^2=4*3.75x}}}

{{{y^2=15x}}}

since the {{{p = 3.75}}} means the focus is {{{3.75 }}}unit to the right of the vertex at coordinate ({{{3.75}}}, {{{0}}})

so, the base should be {{{3.75cm}}} from the target


{{{ drawing( 600, 600, -20, 20, -20, 20,
circle(15,15,.15), locate(15,15,p(15,15)),
circle(15,-15,.15), locate(15,-15,p(15,-15)),
circle(3.75,0,.2), locate(3.75,1.3,F(3.75,0)),
green(line(15,15,15,-15)), locate(15.5,2.5,highlight(green(30))),
graph( 600, 600, -20, 20, -20, 20, sqrt(15x),-sqrt(15x))) }}}