Find the director circle of the parabola x2 + 2y = 4x – 3 .
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The given equation is written as
(x – 2)2 = 1 – 2y = -2(y – 1/2)
Let X = x – 2 and Y = y (1/2). Substituting in above equation we get
X2 = -4aY
where a = 1/2.
The directrix equation Y = a or y − 1 = 0. Therefore, the director circle is the directrix y − 1 = 0.