The required focus of the parabola (x - 1)^2 = 12(y + 2) is (1, 1). Option D is correct.
Given that, equation of the parabola,
A parabola is cross-section cut out of the cone and represented by an equation [tex]y = 4ax^2[/tex]. Where a is focus.
Here,
[tex](x - 1)^2 = 12(y + 2)[/tex]
Simplify the above parabola equation to stand equation
[tex]y = \frac{1}{4(f-k)} (x-h)^2 + k[/tex]
[tex]y =\frac{1}{4(1-(-2))} (x - 1)^2 - 2[/tex]
Now comparing above the equation,
vertex of a parabola,
h = 1 and k = -2
And focus
So the coordinate of the focus of the parabola = (h, f)
= (1, 1)
Thus, the required focus of the parabola (x - 1)^2 = 12(y + 2) is (1, 1). Option D is correct.
Learn more about parabola here:
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