I've been doing revision for my yearlies and I've been struggling with these questions:
1) Prove that, if the difference between the roots of the equation ax^2 + bx + c = 0 is 1, then a^2 = b^2 – 4ac.
2) P is a variable on the curve y = 2x^2 + 3 and O is the origin. Q is the point of the section of OP nearer the origin. Find the locus of Q.
3) Find the equations of the tangents to the curve xy = 6 which are parallel to the line 2y + 3x = 0.
4) The curves y = 2x^2 – x and y^2 = x intersect at (0,0) and at another point Q. Find the angle between the curve at Q.
Could someone please help me out?
Thanx a lot!!!
P.S. I'm really really sorry that I've been posting a lotta questions but I really really need to do good in this exam.