Given the constant a > 0, the straight line passing through the fixed point a (0, a), with m vector = (λ, a) as the direction vector and passing through the fixed point B (0, a), and with n vector = (1,2 λ, a) Where λ belongs to R, the equation for finding the locus C of point P is obtained

Given the constant a > 0, the straight line passing through the fixed point a (0, a), with m vector = (λ, a) as the direction vector and passing through the fixed point B (0, a), and with n vector = (1,2 λ, a) Where λ belongs to R, the equation for finding the locus C of point P is obtained

Let P (x, y), vector AP = (x, y + a), vector BP = (a, Y-A)
∵ vector m is direction vector ∥ vector m ∥ vector AP ∥ AX = λ (y + a) similarly: 2 λ AX = Y-A, λ = (Y-A) / 2aX
Eliminate λ AX = (y + a) * (Y-A) / 2aX 〈 y ^ 2 / A ^ 2-2x ^ 2 = 1 〉 it is a hyperbola