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Lesson: 7.3 Parametric Equations and Locus 参数方程式与轨迹
7.3 Parametric Equations and Locus 参数方程式与轨迹

(1)
Find the equation of the locus of the centers of circles passing through the points of intersection of the circle x + y – 2x – 4y – 11 = 0 and the line y = x + 3.

x + y = 3
(2)
A variable circle touches the y-axis, and also touches a fixed circle x + y – 8x + 2y + 13 = 0 externally. Find the equation of the locus of the centre of the circle.

y – 12x + 2y + 13 = 0
(3)
Find the equation of the locus of the centers of the circles that orthogonal with x + y – 6x + 4y + 5 = 0 and x + y + 2x – 9 = 0.

4x – 2y – 7 = 0
(4)
The equation x + y + ax + by + 7 = 0 represents a unit circle. Find the equation of the locus of its centre as a, b vary.

x + y = 8
(5)
A straight line through the point (0,1) meets the circle C : x + y – 2x – 4y + 4 = 0 at points P, P such that the slope of PP is k. Find the equation of the locus of the mid-point of PP, as k varies.

x + y – x – 3y + 2 = 0
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