# Thread: Equation of the Normal

1. ## Equation of the Normal

Find the equation of the normal to the curve y=3x^2-2x-1 which is parallel to the line y=x-3

2. Originally Posted by creatively12
Find the equation of the normal to the curve y=3x^2-2x-1 which is parallel to the line y=x-3
You want to find the point $\displaystyle (x_0,y(x_0))$ at which $\displaystyle y'(x_0)=-1$.

3. can you please solve the question for me, i couldn't understand what u are saying

12y=12x-17

4. Originally Posted by creatively12
can you please solve the question for me, i couldn't understand what u are saying
No I will not. I don't do that. Sorry.
Now if you what to try to understand how it works, then I will help.
But I will not just hand you the answer.

5. do you know how to find the equation of a line when you are given a point?

6. yes i want to know why we have to calculate the coordinates with the gradient of the tangent and not with the gradient of the normal in this particular question, as i've solved this problem, but after converting the gradient 1 to -1, please tell me that

and thanks for the reply and procedure

7. Originally Posted by creatively12
yes i want to know why we have to calculate the coordinates with the gradient of the tangent and not with the gradient of the normal in this particular question, as i've solved this problem, but after converting the gradient 1 to -1, please tell me that
The slope of the normal line at $\displaystyle (x_0,f(x_0))$ is $\displaystyle \frac{-1}{f'(x_0)}$.

You see the normal is perpendicular to the tangent.

8. Originally Posted by creatively12
can you please solve the question for me, i couldn't understand what u are saying

12y=12x-17
Are you sure this is the answer?

9. Originally Posted by Arturo_026
Are you sure this is the answer?
Yes $\displaystyle 12y=12x-17$ is the correct answer.

10. Originally Posted by Arturo_026
Are you sure this is the answer?
yes

11. but Plato, if we have to find the equation of a normal to a curve that is perpendicular to a line, not parallel, then from which gradient (tangent or normal) would we find the coordinates ??

12. Originally Posted by creatively12
but Plato, if we have to find the equation of a normal to a curve that is perpendicular to a line, not parallel, then from which gradient (tangent or normal) would we find the coordinates ??
No you did not read it very closely.
The normal is perpendicular to the tangent not to the given line.
So that case you are finding where the tangent to the curve is perpendicular to the given line.
Recall from basic geometry, two lines perpendicular to the same line, in this case the tangent, are themselves parallel.