The left focus of the ellipse is (√ 3,0), and the right vertex is d (2,0). Let a (1,1 / 2) be a moving point on the ellipse. If P is a moving point on the ellipse, find the trajectory equation of the midpoint m of the line PA

The left focus of the ellipse is (√ 3,0), and the right vertex is d (2,0). Let a (1,1 / 2) be a moving point on the ellipse. If P is a moving point on the ellipse, find the trajectory equation of the midpoint m of the line PA

The left focus is (√ 3,0), and the right vertex is d (2,0)
So C ^ 2 = 3
a^2=4
So B ^ 2 = 4-3 = 1
x^2/4+y^2=1
Let P (m, n)
Then x = (M + 1) / 2, y = (n + 1 / 2) / 2
So m = 2x-1
n=2y-1/2
P is on the ellipse
So m ^ 2 / 4 + n ^ 2 = 1
(2x-1)^2/4+(2y-1/2)^2=1

Given that the ellipse x ^ 2 / 2 + y ^ 2 = 1, (1) the left focus F of the ellipse leads to the secant of the ellipse, find the trajectory equation of the midpoint P of the cut chord, (2) find the path with slope 2
Trajectory equation of the midpoint Q of parallel string

(1) C = 1, P (x, y) XA + XB = 2x, Ya + Yb = 2yk (AB) = K (PF) (Ya Yb) / (XA XB) = Y / (x + 1) [(XA) ^ 2 / 2 + (ya) ^ 2] - [(XB) ^ 2 / 2 + (Yb) ^ 2 = 1-1 = 0 (XA + XB) * (XA XB) / 2 + (Ya + Yb) * (Ya Yb) = 02x / 2 + 2Y * (Ya Yb) / (XA XB) = 00.5x + y * y / (x + 1) = 0 (x +