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)

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

∵ 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)

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step-by-step explanation:

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

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