And this referred point is called the pole. Pole and Polar: For a point lying outside the parabola, the locus of the points of intersection of the tangents, draw at the ends of the chords, drawn from this point is called the polar. For a point \((x_1, y_1)\) outside the parabola, the equation of the chord of contact is \(yy_1 = 2x(x x_1)\). \(\sqrt(x - x_1)\)Ĭhord of Contact: The chord drawn to joining the point of contact of the tangents drawn from an external point to the parabola is called the chord of contact. We need to derive the equation of parabola using PF = PB The equation of the directtrix is x a = 0 and we use the perpendicular distance formula to find PB. The coordinates of the focus is F(a,0) and we can use the coordinate distance formula to find its distance from P(x, y) Here we consider a point B on the directrix, and the perpendicular distance PB is taken for calculations.Īs per this definition of the eccentricity of the parabola, we have PF = PB (Since e = PF/PB = 1) As per the definition of a parabola, the distance of this point from the focus F is equal to the distance of this point P from the Directrix. Let us consider a point P with coordinates (x, y) on the parabola. The eccentricity of a parabola is equal to 1. It is the ratio of the distance of a point from the focus, to the distance of the point from the directrix. The endpoints of the latus rectum are (a, 2a), (a, -2a). The length of the latus rectum is taken as LL' = 4a.
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