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Dmitry [639]
2 years ago
14

A N S W E R Q U I C K P L E A S E

Mathematics
1 answer:
chubhunter [2.5K]2 years ago
5 0

Answer:

1. A

2. D

3. D

Step-by-step explanation:

The standard form of a parabola is

y=\frac{1}{4p}(x-h)^2+k            ..... (1)

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

1. The directrix of a parabola is y=−8 . The focus of the parabola is (−2,−6) .

k-p=-8                   ...(a)

(h,k+p)=(-2,-6)

k+p=-6            .... (b)

h=-2

On solving (a) and (b),  we get k=-7 and p=1.

Put h=-2, k=-7 and p=1 in equation (1).

y=\frac{1}{4(1)}(x-(-2))^2+(-7)

y=\frac{1}{4}(x+2)^2-7

Therefore option A is correct.

2 The directrix of a parabola is the line y=5 . The focus of the parabola is (2,1) .

k-p=5                   ...(c)

(h,k+p)=(2,1)

k+p=1            .... (d)

h=2

On solving (c) and (d),  we get k=3 and p=-2.

Put h=2, k=3 and p=-2 in equation (1).

y=\frac{1}{4(-2)}(x-(2))^2+(3)

y=-\frac{1}{8}(x-2)^2+3

Therefore option D is correct.

3. The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3 .

k-p=-3                   ...(e)

(h,k+p)=(0,-2)

k+p=-2            .... (f)

h=0

On solving (e) and (f),  we get k=-2.5 and p=0.5.

Put h=0, k=-2.5 and p=0.5 in equation (1).

y=\frac{1}{4(0.5)}(x-(0))^2+(-2.5)

y=\frac{1}{2}(x)^2-2.5

y=\frac{1}{2}(x)^2-\frac{5}{2}

Therefore option D is correct.

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<span> </span>

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Answer:

B and C work. A and D do not.

Step-by-step explanation:

This is one of those questions that you have to go through each answer to see what the results are. You don't have to go far to eliminate A and D so let's do that first.

A]

5n + 6

Let n = 1

5(1) + 6

5 + 6= 11

However there is trouble beginning with n = 2

5*2 + 6

10 + 6

16     All you need is one wrong answer and the choice is toast. So A won't work.

================

Try D

6(n - 1)+ 5

n=0

6*(-1) + 5

-6 + 5

- 1

And D has been eliminated with just 1 attempt. n= 2 or n = 1 would be even worse.  D is not one of the answers.

=============

B

Let n = 1

6(1) + 5

6 + 5

11 The first term works.

n = 2

6*(2) + 5

12 + 5

17 and n = 2 works as well. Just in case it is hard to believe, let's try n = 3 because so far, everything is fine.

n = 3

6*(3) + 5

18 + 5

23 And this also works. I'll let you deal with n = 4

========

C

n = 0

6(0 + 1) + 5

6*1 + 5

6 + 5

11

n = 1

6(1 + 1) + 5

6*2 + 5

12 + 5

17 which works.

So C is an answer.

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