The focus of a parabola is $(1, 2)$ and the point of intersection of the directrix and axis is $(2, 3)$ . Then the equation of the parabola is

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${(x - 1)}^{2} + {(y - 2)}^{2} = \frac{1}{4} {(x + y - 5)}^{2}$

${(x - 1)}^{2} + {(y - 2)}^{2} = \frac{1}{2} {(x + y - 5)}^{2}$

${(x - 1)}^{2} + {(y - 2)}^{2} = \frac{1}{25} {(x + y - 5)}^{2}$

${(x - 1)}^{2} + {(y - 2)}^{2} = \frac{1}{5} {(x + y - 5)}^{2}$

answer is B.

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Detailed Solution

$\begin{array}{l} S (1, 2), Z (2, 3); D i r e c t r i x y - 3 = - 1 (x - 2), \\ N o w u s e S P^{2} = P M^{2} \end{array}$

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