Figure 5 : Parabola Draw tangent using reflection

Read Instructions

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How to draw tangent to parabola by reflection law

• Draw a paraboa of y = a*x^2 + b*x +c.
• Find vertex xv=-b/(2*a).
• Find focus F to directrix D = 1/(2*a)
• Find focus F at xf = xv + D/2.
• Draw a point P on curve.
• Joint P and F.
• Draw line PQ parallel to pricipal axis.
• Bisect angle FPQ.
• Draw line perpendicular to bisection and passing P
• This is the tangent.

Keywords : PF = P to directirx is parabola

Defintion Reflection law of parabola. Source at focus F, parabola will reflect light parallel to princial axis. Bisector is normal and incident angle equals reflect angle. Equation of parabola y + D/2 = x^2/(2*D). Focus F is origin. D is distance from focus to directirx. f is the focal length and f = Sqr(a^2 - b^2). The focus is on line x = 0 which is the principal axis.

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