Hey! STEP III, 2004, Q8 under consideration here.
I got the general solution as
y2=2x+Ax2 (correct)
Then
(1,1):y2=2x−x2(2,2):y2=2x(4,4):y2=2x−2x2The (1,1), (2,2) check out when replacing x with two and square rooting, but for the third one (4,4) - if I replace x=4 into there, I get y=0. So, I must be doing something wrong, can anybody see what?
Also, the first equation is a circle of radius 1 centre (1,0), right?
The second is a typical square root graph?
Using the form given up there, I got the third as being an ellipse - but it can't be correct since it doesn't pass through (4,4) - I'm tearing my hair out here!