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Binomial Theorem
The focus is S(6, 0) which lies on xaxis.
The directrix is x + 6 = 0 which is a line parallel to yaxis i.e., perpendicular to xaxis.
∴ The parabola is of the standard form
Also, focus (a, 0) (6, 0) directrix x + a = 0 is x + 6 = 0 a = 6
Hence, the equation of the parabola is
Alternative method:
Let line l be the directrix with equation x + 6 = 0
The focus is S (6, 0). Take a point on the parabola.
From P, draw PM perpendicular on directrix l and join PS. By definition of parabola, PS = PM
d = p
Squaring both sides, we get
Hence, the locus of P i.e., the equation of parabola is
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