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25 August, 05:32

Given the information below, write the equation in Standard Form.

Parabola:

Vertex (3, - 2)

Focus (5, - 2)

+2
Answers (1)
  1. 25 August, 07:24
    0
    The standard form of the equation of the parabola is (y + 2) ² = 8 (x - 3)

    Step-by-step explanation:

    The standard form of the equation of a parabola is (y - k) ² = 4p (x - h), where

    The vertex of the parabola is (h, k) The focus is (h + p, k)

    ∵ The vertex of the parabola is (3, - 2)

    ∴ h = 3 and k = - 2

    ∵ The focus is (5, - 2)

    ∴ h + p = 5

    - Substitute h by 3 to find p

    ∵ 3 + p = 5

    - Subtract 3 from both sides

    ∴ p = 2

    ∵ The standard form of the equation of the parabola is (y - k) ² = 4p (x - h)

    - Substitute the values of h, k, and p in the equation

    ∴ (y - - 2) ² = 4 (2) (x - 3)

    ∴ (y + 2) ² = 8 (x - 3)

    The standard form of the equation of the parabola is (y + 2) ² = 8 (x - 3)
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