Which of the following can be the parametric equation of $(x - 1)^{2} = - 36 (y - 4)$

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Solution

The parametric equation of
$x^{2} = - 4 a y$ are $x = 2 a t$ and $y = - a t^{2}$

$\Rightarrow For (x - 1)^{2} = - 4 \times 9 (y - 4)$ ,
Where $X = x - 1, a = 9, Y = y - 4$
So, $X = 2 a t and Y = - a t^{2}$
$x - 1 = 2 \times 9 \times t and y - 4 = - 9 t^{2}$

$\Rightarrow x = 1 + 18 t and y = 4 - 9 t^{2}$
Hence, the correct answer is Option a.

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