The equation of the parabola that has a vertex (2 , -1) and a directrix
of x = 5 is (y + 1)² = -12(x - 2)
Step-by-step explanation:
Let us revise the equation of a parabola
1. The form of the equation is (y − k)² = 4p(x − h)
2. The coordinates of its vertex are (h , k)
3. The equation of its axis of symmetry is y = k
4. The coordinates of the focus are (h + p , k)
5. The directrix is at x = h − p
∵ The coordinates of the vertex of the parabola are (2 , -1)
∵ The coordinates of its vertex are (h , k)
∴ h = 2 and k = -1
∵ The directrix is at x = 5
∵ The directrix is at x = h − p
∴ h - p = 5
∵ h = 2
∴ 2 - p = 5
- Subtract 2 from both sides
∴ - p = 3
- Multiply both sides by -1
∴ p = -3
∵ The form of the equation is (y − k)² = 4p(x − h)
∴ (y - -1)² = 4(-3)(x - 2)
∴ (y + 1)² = -12(x - 2)
The equation of the parabola that has a vertex (2 , -1) and a directrix
of x = 5 is (y + 1)² = -12(x - 2)
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You can learn more about equation of a parabola in brainly.com/question/8054589
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