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construction of Parabola When Distance between directrix and focus is given

If distance between focus and directrix is 2a , then equation of parabola is  y2 = 4 a x

Hence for a given x-coordinate , y-coordinate of points on parabola are

For various value of x , we calculte the y-coordinate , mark these points (x,y)  on x-y plot , then join these points by smooth curve.

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For example , let given distance between focus and directrix is 2 .

Hence , 2a = 2  and   a = 1 .

Hence the parabola is y2 = 4x

Following tables gives the x and y coordinates of different points on parabola

 x y O 0 0 A 1 +2.0 A' 1 -2.0 B 2 +2.8 B' 2 -2.8 C 3 +3.5 C' 3 -3.5 D 4 +4.0 D' 4 -4.0

Above points are plotted on x-y plot given below and joined by smooth curve to get the parabola y2 = 4x

Answered by Thiyagarajan K | 22 Dec, 2023, 04:14: PM

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