Just a note, you should really be providing working out (anything that you've done at all!) so we can help you better! I'm not gonna give a full answer just yet (I used to do that but it doesn't really help you learn), but feel free to enquire further!
For Q1, note that from Pythagoras' Theorem the distance from (-1, 2) to the origin is the square root of 5 and similarly the distance from (3, 4) to the origin is 5. Then, using two distance formulae and equating, let the distance from (-1, 2) to the point P(x, y) be d and the distance from (3, 4) to P(x, y) be root 5 x d. Then, for distance d, the distance from (-1, 2) x square root of 5 = distance from (3, 4) for any point P(x, y) on the locus. See how you go from there.
For Q2, I haven't actually found a 'proper' 2U method of doing this. (Someone please give a proper answer w/ working out, help me out here!
) I guess I'll give the answer for this one because I did this one on intuition. Basically A is the point (4, 0) or (-4, 0). Also, these points themselves have to lie on the locus (chords from A to A 'count'). Also, the origin is on the locus as well, drawing from (4, 0) to (-4, 0). Drawing to both A's from (0, 4) and (0, -4) makes two diamond shapes and at this point most people think what the hell is this locus?
Draw a few more chords and you'll start to see it, or if it already made sense, there's nothing else it can possible be except two circles (mainly because of the way the circle is shaped (ask me more if you dont get it.)) Basically it's two circles radius 2 with their centres at (-2, 0) and (2, 0), side by side.
For Q3, intuitively it's just another circle. What you actually have to do is find the radius of the circle, since the centre of the circle will be the same. So for this one, I suggest completing the square to find the centre, then considering in one case where the midpoint of the chord is in relation to the centre of the circle, I think you should be able to find the radius.
Hope this helped!
Home
Help
Search
Login
