Given that point P is a moving point on circle C: x ^ 2 + y ^ 2 + 2x = 0, a (1,0), and that the vertical line of line PA intersects the straight line PC at point m, then the trajectory equation of point m is

Given that point P is a moving point on circle C: x ^ 2 + y ^ 2 + 2x = 0, a (1,0), and that the vertical line of line PA intersects the straight line PC at point m, then the trajectory equation of point m is

We can take advantage of the fact that P is the intersection of circle and X-axis to get m (1 / 2,0), (- 1 / 2,0), which is the vertex of hyperbola. Let's look at the tangent Pb and PD of circle C from a respectively. It is obvious that the perpendicular of PA is parallel to PC, and there is no intersection. This is the asymptote of M curve. It is easy to get: BC = 1, AC = C, ab = √ 3, asymptote equation y = ± √ 3