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4. The directrix of the parabola 12(y + 3) = (x-4)2 has the equation y=-6. Find the coordinates of
the focus of the parabola.

Respuesta :

Ashraf82

The coordinates of the focus of the parabola are (4 , 0)

Step-by-step explanation:

The standard form of the equation of the parabola is  

(x - h)² = 4p(y - k), where

  • The vertex of the parabola is (h , k)
  • The focus is (h , k + p)
  • The directrix is at y = k - p

∵ The equation of the parabola is 12(y + 3) = (x - 4)²

 - The form of the equation is (x - h)² = 4p(y - k), compare

    between them to find h, k and p

∴ h = 4

∵ - k = 3

- Multiply both sides by -1

∴ k = -3

∵ 4p = 12

- Divide both sides by 4

∴ p = 3

∵ The coordinates of the focus are (h , k + p)

∵ h = 4 , k = -3 , p = 3

∴ k + p = -3 + 3

∴ k + p = 0

∴ The focus is (4 , 0)

The coordinates of the focus of the parabola are (4 , 0)

Learn more:

You can learn more about the equation of the parabola in brainly.com/question/9390381

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