Let P(a,a² ) be any point on the curve y=x² , then the line ℓ through P with gradient m has an equation y-a² =m(x-a). Show the x coordinates of the points where ℓ meets the curve are x=a and x=m-a. Find the value of m for which these two points coincide, and explain why it follows that the derivative of x² is 2x.
I solved y=x² and y-a²^=m(x-a) simultaneously to get x = a , x= m-a.
I'm confused how to solve the last part of the question, since this is worded strangely as well.
I solved y=x² and y-a²^=m(x-a) simultaneously to get x = a , x= m-a.
I'm confused how to solve the last part of the question, since this is worded strangely as well.