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2 years ago

Find the equation of the parabola with focus (2, 3) and directrix y = -1. es

Mathematics

2 answers:

aev [14]2 years ago

7 0

Y=1/8^2-1/2x + 3/2 would be the answer

Elan Coil [88]2 years ago

4 0

Answer:

Below in bold.

Step-by-step explanation:

Let (x, y) be a point on the parabola. As the graph is a parabola, the distance of this point to the focus is equal to the distance of this point from the directrix. So:

√(( x - 2)^2 + (y - 3)^2) = y - (-1)

Squaring both sides:

(x - 2)^2 + (y - 3)^2 = (y + 1)^2

x^2 - 4x + 4 + y^2 - 6y + 9 = y^2 + 2y + 1

x^2 - 4x + 4 + 9 - 1 = 2y + 6y

8y = x^2 - 4x + 12

y = 1/8(x^2 - 4x + 12)

or we can write it as

y = 1/8x^2 - 1/2 x + 3/2.

You might be interested in

What is the simplified form of x plus 4 over x squared minus 3x minus 10⋅x minus 3 over x squared plus x minus 12? (6 points)

melomori [17]

Answer:

The simplified form is 1 over the quantity x plus 2 times the quantity

x minus 5 ⇒ 1/(x+2)(x-5) ⇒ last answer

Step-by-step explanation:

* Lets write the product of the two fraction

∵ $\frac{x+4}{x^{2}-3x-10} *\frac{x-3}{x^{2}+x-12}$

- At first factorize the denominators

# x² - 3x - 10

∵ x² = x × x ⇒ 1st term in the 1st bracket and 1st term in the

2nd bracket

∵ -10 = 2 × -5 ⇒ 2nd term in the 1st bracket and 2nd term in the

2nd bracket

∵ x × - 5 = -5x ⇒ ext-reams

∵ x × 2 = 2x ⇒ means

∵ 2x + -5x = -3x ⇒ middle term

∴ x² - 3x - 10 = (x + 2)(x - 5)

# x² + x - 12

∵ x² = x × x ⇒ 1st term in the 1st bracket and 1st term in the

2nd bracket

∵ -12 = -3 × 4 ⇒ 2nd term in the 1st bracket and 2nd term in the

2nd bracket

∵ x × 4 = 4x ⇒ ext-reams

∵ x × -3 = -3x ⇒ means

∵ 4x + -3x = x ⇒ middle term

∴ x² + x - 12 = (x - 3)(x + 4)

* Lets write the fractions after factorization

∴ $\frac{x+4}{(x+2)(x-5)}*\frac{x-3}{(x-3)(x+4)}$

- lets simplify the fractions by cancel (x - 3) up with (x - 3) down

and cancel(x + 4) up with (x + 4) down

∴ $\frac{1}{(x+2)(x-5)}*1=\frac{1}{(x+2)(x-5)}$

* The simplified form is 1 over the quantity x plus 2 times the

quantity x minus 5

3 0

2 years ago

How much is 20 times 96

Iteru [2.4K]

Answer:

1920

Step-by-step explanation:

Hope this helps :)

4 0

3 years ago

Read 2 more answers

What is the surface area of the triangles prism?? 13 points please give the right answer

MrMuchimi

First, let's calculate the triangles of the prism.

The area of a triangle is base times height, then divide by 2.

So:

(7*8)/2.

This would give us 28.

Also knowing that there are two triangles on the prism, we have to multiply 28 by 2. This would give us 56.

Now, for the rectangles, we have to find their areas.

The area of a rectangle is length times width. So this would give us:

8*16.

This equals 128.

Next, knowing that there are three rectangles, multiply 128 by three. This gives us 384.

Now, we jus have to add all the areas together:

384+56 = 440

So the prism's surface area is 440cm^2

Hope this helps. If you have any questions, please put them in the comments below.

6 0

3 years ago

If f(x) = 5x – 1, then f^-1(x)=

adell [148]

Step-by-step explanation:

f(x) = 5x – 1

To find the inverse equate f(x) to y

That's

f(x) = y

y = 5x - 1

Interchange the terms

x = 5y - 1

Make y the subject

we have

5y = x + 1

Divide both sides by 5

y = x+1/5

Therefore f^-1(x)= x + 1/5

Hope this helps you

3 0

3 years ago

Can you solve number 74 plzzzzzzzzzzzzzzzzzzz

Mila [183]

The answer would be graph b.
It would be graph b because the point would be five to the left(West) and two down(South).

3 0

2 years ago