## zaphod 3 years ago Find the equation of the normal to the curve y = 3x^2-2x-1 which parellel to the line y = x-3

1. zaphod

@sauravshakya @TuringTest @satellite73

2. Algebraic!

find y', set it equal to -1 and solve for x; that's an x coord. on your line. plug into y = 3x^2-2x-1to get a y coord. you have a point and the slope now.. find the line?

3. myko

1º. Find the derivative of y 2º Put it in some form you like (slope intercept, general...) 3º change it's direction vector to perpendicular 4º find x, for which it's slope is 1

4. zaphod

i got the points, why is the slope 1, it has to be -1 since we take the normal line?

5. Algebraic!

if slope of the tangent = -1, slope of the normal =1.

6. zaphod

can u show it in a diagram?

7. Algebraic!

|dw:1347988256856:dw|

8. zaphod

i cant picture the problem clearly?

9. zaphod

@Algebraic! where the parellel like y=x-3?

10. Algebraic!

wut

11. zaphod

can u show the parellel line y =x-3 in the diagram?

12. Algebraic!

|dw:1347988441351:dw|

13. Algebraic!

this was just a general sketch to illustrate the point. this isn't your parabola. but that's the line x-3 in black

14. zaphod

why cant we directly get the gradient as m=1 instead of -1

15. Algebraic!

try it and see

16. zaphod

im getting a different answer and the answer is wrong

17. Algebraic!

18. zaphod

4y =2x-5

19. zaphod

dy/dx= 6x - 2 6x - 2 = 1 x= 1/2 y= -5/4

20. zaphod

cn u shw the working

21. Algebraic!

find y', set it equal to -1 and solve for x; that's an x coord. on your line. plug into y = 3x^2-2x-1to get a y coord. you have a point and the slope now.. find the line?

22. zaphod

why do we set it equal to -1 instead of 1?

23. Algebraic!

you don't like negative one so you went with one instead? and got the wrong answer?

24. Algebraic!

when the tangent to the parabola has a slope of -1, the normal at that point has a slope of 1

25. zaphod

i got it thanks :)