For curve =2x^2−5x+2 , if the normal to the curve at point is parallel to the tangent to the curve when =2 , find the co-ordinates of

Question

I'm struggling on the above question.

I have dy/dx as 4x-5 gradientTangent = 3 gradient normal = -1/3

the corresponding y co-ordinate at x=2 is y=0

I have also created the eqn of the tangent and the normal at this point but I don't really understand what the question is asking for or how to find P.

Answer 1

Now for $x_P$ we have $$4x-5=-\frac{1}{3},$$ which gives $$x_P=\frac{7}{6}.$$ Can you end it now?

I got $$P\left(\frac{7}{6},-\frac{10}{9}\right).$$