PARABOLA
Definition : A parabolla is the locus of the point in plane equidistant from a fixed point and a fixed line in that plane . The fixed point is called the focus and the fixed straight line is called the directrix. Standard Equation Of The Parabola : Equation of the parabola in the standard form y 2 = 4ax. Let S be the focus and d be the directrix of the parabola . Let SZ be perpendicular to the directrix . Bisect SZ at the point O. By the definition of parabola the midpoint O is on the parabola. Take O as the origine , line OS as the X- axis and and the line through O perpendicular to OS as the Y-axis . Let SZ = 2a , a > 0 . Then the coordinates of the focus S are (a, 0) and the coordinates of Z are (-a, 0). The equation of the directrix d is x = -a , i.e. x + a = 0 Let P(x, y) be any point on the parabolla . Draw segment PM perpandicular to the directrix d . ∴ M = (-a, y) By using distance formula we have By focus - directrix property of the parabolla SP = PM Squaring bo