Let A and B be two fixed points. P is a moving point.
What is the locus (geometric meaning, eg circle, ellipse...) of(1) PA = 2 PB(2) 3PA = 2PB(3) PA + PB = 2(4) PA - PB = 2Let F be a fixed point. P is a moving point.
(5) What is the locus (geometric meaning, eg circle, ellipise...) of
distance between P and F equal to distance between P and a fixed straight line?(6) Ax^2 + By^2 + Cxy + Dx + Ey + F = 0, 點樣由 coefficient 睇到條 equation 係 conics 裡的 circle, parabola, ellipse or hyperbola?
- 翻雷滾天 風卷殘雲Lv 79 年 前最佳解答
(1) and (2): Circle
For any positive value of k NOT equal to 1, when PA = k PB, the locus describes a circle
Ellipse is a locus of moving point so that the SUM of its distances from two fixed points, known as foci, is a constant.
Hyperbola is a locus of moving point so that the DIFFERENCE of its distances from two fixed points, known as foci, is a constant.
Parabola is a locus of moving point so that the distance from it to a fixed point (known as focus) is always equal to that from it to a fixed line (known as directrix)
(6) Obviously when C = 0 and A = B, it will be a circle
Then for other situations, we have to check the sign (positive or negative) of the value AB - (C/2)^2.
If AB - (C/2)^2 = 0, then it is a parabola
If AB - (C/2)^2 > 0, then it is an ellipse
If AB - (C/2)^2 < 0, then it is a hyperbola資料來源： 原創答案