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Axis of Symmetry of a Parabola

Result

line | through (f_x, f_y)
through (v_x, v_y)
(assuming focus (f_x, f_y) and vertex (v_x, v_y))

Visual representation


(drawn with rotation angle 0°)

Equation forms

y = (x (f_y - v_y))/(f_x - v_x) + (-f_y v_x + f_x v_y)/(f_x - v_x)

y - f_y = ((x - f_x) (f_y - v_y))/(f_x - v_x)

y (f_x - v_x) + f_y v_x - f_x v_y + x (v_y - f_y) = 0
(assuming focus (f_x, f_y) and vertex (v_x, v_y))

Properties of axis of symmetry

x-intercept | (f_y v_x - f_x v_y)/(f_y - v_y)
y-intercept | (f_x v_y - f_y v_x)/(f_x - v_x)
slope | (f_y - v_y)/(f_x - v_x)
(assuming focus (f_x, f_y) and vertex (v_x, v_y))

Distance

from (f_x, f_y) to (v_x, v_y): sqrt((f_x - v_x)^2 + (f_y - v_y)^2)

Midpoint

between (f_x, f_y) and (v_x, v_y): (1/2 (f_x + v_x), 1/2 (f_y + v_y)) = (0.5 (f_x + v_x), 0.5 (f_y + v_y))

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