Question

The vertex of a parabola is (6,2), and the equation of its directrix is x = 8. What is the equation of this parabola in standard form?

a. (y−2)2=8(x−6)

b. (y−2)2=−8(x−6)

c. (x−6)2=−8(y−2)

d. (x−6)2=8(y−2)

Answer 1

Answer:

The equation of this parabola in standard form is (y - 2)² = -8(x - 6) ⇒ B

Step-by-step explanation:

Let us revise the standard form of the equation of a parabola

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

• (h, k)  is the turning point

• (h + p, k)  are the coordinates of the focus

• x = h - p  is the equation of the directrix

∵ The vertex of a parabola is (6, 2)

→ From the fact above

∴ h = 6 and k = 2

∵ The equation of its directrix is x = 8

→ From the fact above

∴ h - p = 8

→ Substitute the value of h to find p

∵ 6 - p = 8

→ Subtract 6 from both sides

∴ - p = 2

→ Multiply both sides by -1

∴ p = -2

→ Substitute the values of h, k, and p in the form above

∴ (y - 2)² = 4(-2)(x - 6)

∴ (y - 2)² = -8(x - 6)

∴ The equation of this parabola in standard form is (y - 2)² = -8(x - 6)