The equation of the parabola whose vertex is (-1, -2) axis is vertical and which passes through the point (3, 6) is

x^{2} + 2 x - 2 y - 3 = 0

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2 x^{2} = 3 y

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x^{2} - 2 x - y + 3 = 0

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None of these

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Solution

The correct option is A $x^{2} + 2 x - 2 y - 3 = 0$
Since the axis is vertical, the equation of the parabola would be of the form $X^{2} = 4 A Y$
Since the vertex is (-1,2), the equation will be
$(x + 1)^{2} = 4 a (y + 2)$
To find a,
parabola passes through $(3, 6) \Rightarrow 16 = 4 a .8 \Rightarrow a = \frac{1}{2}$
$\Rightarrow (x + 1)^{2} = 2 (y + 2) \Rightarrow x^{2} + 2 x - 2 y - 3 = 0.$

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