Question

Write the equation for a parabola with a vertex of (-5,-4) and a focus of (-5,-2)

Answer 1

The equation of the parabola is (x + 5)² = 8(y + 4)

Step-by-step explanation:

Let us revise the equation of the parabola in standard form

• The standard form is (x - h)² = 4p(y - k)
• The vertex is (h , k)
• The focus is (h, k + p)

∵ The vertex of the parabola is (-5 , -4)

- The coordinates of the vertex are (h , k)

∴ h = -5 and k = -4

∵ The focus is (-5 , -2)

- The focus is (h , k + p)

∴ k + p = -2

∵ k = -4

∴ -4 + p = -2

- Add 4 to both sides

∴ p = 2

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

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

∴ (x - -5)² = 4(2)(y - -4)

∴ (x + 5)² = 8(y + 4)

The equation of the parabola is (x + 5)² = 8(y + 4)

Learn more:

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

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