A parabola is drawn with focus at $(3, 4)$ and vertex at the focus of another parabola $y^{2} - 12 x - 4 y + 4 = 0$ . Then equation of the parabola is

x^{2} - 6 x - 8 y + 25 = 0

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y^{2} - 8 x - 4 y + 28 = 0

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x^{2} - 6 x + 8 y - 25 = 0

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x^{2} - 4 x - 8 y + 28 = 0

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Solution

The correct option is A $x^{2} - 6 x - 8 y + 25 = 0$
$y^{2} - 12 x - 4 y + 4 = 0$

${(y - 2)}^{2} = 12 x$

Vertex is $(0, 2)$ and $a = 3$

The focus of parabola is $(3, 2)$

Hence the vertex of required parabola is $(3, 2)$ and focus is $(3, 4),$ then

$a = \sqrt{0 + 2^{2}} = 2$

So required parabola is ${(x - 3)}^{2} = 4 (2) (y - 2)$

$\Rightarrow x^{2} - 6 x - 8 y + 25 = 0$

Hence, option 'A' is correct.

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