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RideAnS [48]
3 years ago
7

Write the equation for a parabola that has a vertex (2, -1) and a directrix of x = 5.

Mathematics
2 answers:
Andreas93 [3]3 years ago
7 0

Answer:

B

2, -1

x = h - p

-3

C

Step-by-step explanation:

Edge2020 :)

Alika [10]3 years ago
3 0

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)

Learn more:

You can learn more about equation of a parabola in brainly.com/question/8054589

#Learnwithbrainly

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