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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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Answer:

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Step-by-step explanation:

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<u>Cost of buffalo:</u>

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<u>Answer is:</u> Rs. 112000

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3 years ago
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After my salary was increased by $16\%,$ it was $\$52{,}200$. What was my salary before the increase?
boyakko [2]
The salary before the increase was $48000.
5 0
2 years ago
How can I solve this?
Eva8 [605]

Answer:

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and in a triangle, interior angles add to 180 so 47+x+y=180

90 + 43 = 133

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so your answer is a

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8 0
3 years ago
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the en
GuDViN [60]

Answer:

P = 0.1447

Step-by-step explanation:

Given

n = 7000 -- total

d = 180 --- defective

r = 6 --- selected

Required

The probability of rejecting the batch

This means that at least one of the selected piece is defected.

So, we first calculate the probability that all the selected piece are accepted.

So, we have:

Pr = \frac{7000 - 180}{7000} * \frac{6999 - 180}{6999}* \frac{6998 - 180}{6998}* \frac{6997 - 180}{6997}* \frac{6996 - 180}{6996}* \frac{6995 - 180}{6995}

The denominator decreases by 1 because it is a probability without replacement; 180 is subtracted from the numerator to represent the number of non-defective CDs

So, we have:

Pr = \frac{6820}{7000} * \frac{6819}{6999}* \frac{6818}{6998}* \frac{6817}{6997}* \frac{6816}{6996}* \frac{6815}{6995}

Pr = 0.8553

Using the complement rule, the probability that the batch will be rejected is:

P = 1 - 0.8553

P = 0.1447

8 0
2 years ago
For breakfast, Clarissa can choose from oatmeal, cereal, French toast, or scrambled eggs. She thinks that if she selects a break
makvit [3.9K]

Clarissa is not correct. If she were to choose one from the stack at random, it means that she has a 25%, or a 1/4 chance to pick the oatmeal, just like the other breakfast items.

If there were to be more oatmeals than any of the other items, it will heighten the chance of her getting oatmeal which would be the only way to make her statement correct.

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3 years ago
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