A parabola can be drawn given a focus of (-4, -5) and a directrix of y=3. Write the equation of the parabola in any form.

The equation of the parabola is (x + 4)² = -16(y + 1)

Step-by-step explanation:

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

∵ The focus at (-4, -5)

∴ h = -4

∴ k + p = -5 ⇒ (1)

∵ The directrix at y = 3

∴ k - p = 3 ⇒ (2)

→ Add equations (1) and (2) to find k

∴ 2k = -2

→ Divide both sides by 2 to find k

∴ k = -1

→ Substitute it in equation (1) to find p

∵  -1 + p = -5

→ Add both sides by 1

∴ -1 + 1 + p = -5 + 1

∴ p = -4

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

∵ (x - -4)² = 4(-4)(y - -1)

∴ (x + 4)² = -16(y + 1)

∴ The equation of the parabola is (x + 4)² = -16(y + 1)

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98