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)

think about it deeply and passionately about this property

i am sorry

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?