A locus of the points which are at an equal distance from a fixed point and a fixed line is called a parabola. The fixed point is called the focus and the fixed line is called the directrix.
The equation of the parabola with focus at P and directrix ax + by + c = 0 is √[(x - x _{1})^{2} + (y - y_{1})^{2}] = (ax_{1} + by_{1} + c)/[√(a^{2} + b^{2})] - The straight line joining any two points on the parabola is called the chord of the parabola.
- The chord of the parabola passing through the focus is called the focal chord of the parabola.
- The distance of a point on a parabola from the focus is called its focal distance.
- A straight line drawn perpendicular to the axis of the parabola and terminated at both ends by the parabola is called a double ordinate.
- The double ordinate passing through the focus of the parabola is called the latus rectum.
The length of latus rectum in all the above cases is 4a. Tangent to the parabola y ^{2} = 4ax at P(x_{1},y_{1}) is yy _{1} = 2a(x + x_{1})The equation of the normal at this point is y - y _{1} = -(y_{1}/2a)(x - x_{1}) The straight line y = mx + c is tangent to the above parabola if m≠0 and c = a/m. |

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