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VladimirAG [237]
3 years ago
7

Which of the following equations describes the set of all points (x, y) that are equidistant from the x-axis and the point (4, 6

)? (A) (x - 4)^2 + (y - 6)^2 = 9 (B) (x - 4)^2 = 12(y - 3) (C) (y - 3)^2 = 12(x - 4) (D) (x - 4)^2 = 6(y - 3) (E) (x - 4)^2 = 12(y - 6) Why is the answer choice (B)? And also, why not choice (D)?
Mathematics
1 answer:
const2013 [10]3 years ago
3 0

Answer

The option B is the right answer because the vertex is (4,3)

Step-by-step explanation:

In the canonical equation of the parabola:

(X-h) ^ 2 = 4p (y-k)

The values (h, k) correspond to the coordinates (x, y) of the vertex.

In the definition of the problem it is said that the guideline of the parabola is the X axis, that is, the line Y = 0 and the focus is the point (4,6).

If the vertex were the point (4.6) the correct option would be option D

But the vertex is located at the midpoint of the segment defined by the focus points (4, 6) and the point (4, 0) that is on the parabola directrix. therefore, as the vertex is the point (4.3). the correct option is B.

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If the point W is the midpoint of SU, then we can conclude that SW equals WU. This means;

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Collect like terms and you now have,

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