Year 12s: what will be the first way you research your future options? >>

Differentiation

Please help me do part iii, I already did part i and ii.

How do i approach the question, i did simultaneous equation for the values of k and the equation of the curve.

Reply 1

ghostwalker

Original post by Jian17

Please help me do part iii, I already did part i and ii.

How do i approach the question, i did simultaneous equation for the values of k and the equation of the curve.

I presume you mean you put each value of k into the equation of the line, and then solve the equation of the line and the curve simultaneously to get the x-coordinate of A,B. And hence the y-coordinate, etc.

That's one way, and barring errors, will work.

Alternatively, for each k, sub into the equation in (i) to get the x-coordinate, then sub into eqn of the curve to get the y-coordinate. Etc.

Edit: Knowing that the two specific values of k give equal roots to equation in (i), since the discriminant is zero, then the quadratic formula will simplify to x=-b/2a.