Tangents of a parabola perpendicular to a line

[phyico]

A Tangent to the parabola y = 3x^2 - 7x + 5 is perpendicular to x + 5y - 10 = 0

Determine the equation of the tangent

i really don't know where to start!

 

[yyat]

What have you tried? Where are you stuck?

 

[wywong]

List sets of parameters that can specify the tangent line. Then see if you can write enough equations to solve the unknowns. E.g.

i. Let the tangent be y=mx+c.

ii. Let the tangent be ax+by+c=0.

iii. Let the point where the tangent touches the parabola be (x1,y1).

Judge for yourself which set is easier, and go on solving it. Sometimes it is hard to tell beforehand and you may need to pick one and switch to another if got stuck.