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)

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

the answers are in the images, i received 100% on this assignment. hope this !