Expert: Paul Klarreich - 3/5/2009

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

Determine the equation of the tangent

thanks.

Answer
Questioner:   Navid
Category:  Calculus
Private:  No
 
Subject:  slope of a Tangent
Question:  A tangent to the parabola y = 3x^2 - 7x + 5 is perpendicular to

x + 5y - 10 = 0.

Determine the equation of the tangent

thanks.
..........................................
Here is what you will do:

1. The line x + 5y - 10 = 0 has slope -1/5, so the line perpendicular to

it has slope m = 5. [Look up slopes of perpendicular lines.]

2. The tangent line will have a slope given by m = y' = 6x - 7.

3. At the proper point, those slopes will be the same, so you can find x0 = 2, then y0 = f(x) at the corresponding point on the parabola.

4. Use the point-slope form (look that up) for the equation of a line; substitute your m,x0,y0, simplify, and you have your answer.

If you get stuck, send me your work and I'll see what I can do.