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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