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umka21 [38]
3 years ago
6

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.

Mathematics
1 answer:
Lady bird [3.3K]3 years ago
3 0

Answer:

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 vertex of the parabola is (h, k)
  • The focus is (h, k + p)
  • The directrix is at y = k - p  

∵ 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)

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pshichka [43]

1. \:  =  > 4( - 7) \\  = 4 \times  - 7 \\  =  - 28

3. \:  =  > 9( - 12) \\  = 9 \times  - 12 \\  =  - 108

4. \:  =  >  - 6( - 8.75) \\  = 6 \times 8.75 \\  = 52.5

5. =  > 27( - 3) \\  = 27 \times  - 3 \\  =  - 81

7. \:  =  >  - 55(0) \\  - 55 \times 0 \\  = 0

8. \:  =  > ( - 7)( - 7.25) \\  = 7 \times 7.25 \\  = 50.75

11. \:  =  > ( - 1) {}^{4}  \\  = 1 {}^{4}  \\  = 1

13. =  > 42 \div ( - 7) \\  =  - (42 \div 7) \\  =  - 6

15. =  >  - 9 \div 3 \\  =  - (9 \div 3) \\  =  - 3

<h2>Solved ✔︎</h2>

8 0
2 years ago
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