The equation of a line through the origin is of the form:Originally Posted bybecky

,

such a line meets the parabola:

when:

,

and if the line is a tangent this last equation has a single root

(since in general a line cuts a parabola at two points, one point

or no points, the one point case is a tangent).

Rearranging the equation gives:

,

and this has a single root when its discriminant is zero:

,

this is because a general quadratic equation has

roots , and both

of the roots are coincident (ie there is only one root) when

.

Solve this for and then plug these solutions back into the

equation of a line through the origin to get the equations for all

the the tangents to the parabola which pass through the origin.

RonL