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Brums [2.3K]
3 years ago
10

Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8.

Mathematics
2 answers:
Reil [10]3 years ago
7 0

In this problem, given the focus at (2,4) and directrix at y = 8. then it is implied that the parabola is facing downwards. The vertex hence is at the middle of the focus and the directrix, hence at (2, 6). The general formula of the parabola is y-k = -4a  ( x-h)^2. Substituting, y -6 = -1/8 *(x-2)^2. Answer is A. 
Mrac [35]3 years ago
7 0
Hello,

y=ax^2+b+c\\

\Delta=b^2-4ac\\

Focus=(- \dfrac{b}{2a}, \dfrac{1-\Delta}{4a} ) \\

Directrix=y=- \dfrac{1+\Delta}{4a} \\

- \dfrac{b}{2a}=2==\textgreater\ b=-4a\\

 \dfrac{1-\Delta}{4a}=4==\textgreater\ \Delta=1-16a\\

- \dfrac{1+\Delta}{4a}=8==\textgreater\ \Delta=-1-32a\\

1-16 a=-1-32a==\textgreater\ a=- \dfrac{1}{8} \ ,\ b=-4a= \dfrac{1}{2} \\

\Delta=-32a-1=3\\

b^2-4ac=3= \dfrac{1}{4}+ \dfrac{1\ c}{2}  ==\textgreater\ c= \dfrac{11}{2} \\


y=- \dfrac{1}{8}x^2+ \dfrac{1}{2} x+ \dfrac{11}{2}  \\


 



\boxed{y=- \dfrac{1}{8}(x-2)^2+6}

Vertex is in the middle of directrix and focus on the axis of symmetry.

Answer A
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Hunter-Best [27]

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(not completely sure though, I'm not the brightest)

Step-by-step explanation:

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2 years ago
The area of a circle is 78.5 cm² . Find the lenght of the radius of a circle . Use π = 3.14
Tpy6a [65]

Answer:

5cm  = r

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

78.5 = 3.14 r^2

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78.5/ 3.14 = r^2

25 = r^2

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3 years ago
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What is 9x-5-8+x= what
Elanso [62]
Hi there!

First you simplify.

Simplified = 9x+(−5)+(−8)+x

Then you combine the like terms.

<span><span><span><span><span>9x</span>+(<span>−5)</span></span>+(<span>−8)</span></span>+x (*-5 and -8 are like terms) (9x and x are like terms)

</span></span><span><span><span>Combined it's~ (<span><span>9x</span>+x</span>)</span>+<span>(<span><span>−5</span>+<span>−8</span></span>)

</span></span></span><span><span><span>Solve and that comes to 10x</span>+<span>−<span>13 which is your answer. :)

Hope this helps. 

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3 0
3 years ago
HELP ASAP!!! PLEASE CHECK ALL OF THEM!
pochemuha

Answer:

2.

A. (P+h)(x)

2x/x+4 (x-1) + x/x-1 (x+4)

2x^2-1/x^2-4

+

X^2+4/x^2-4

= 3x^2+3/x^2-4

B. (F-g)(x)

X^2-7x+6-x - 6

= x^2 -8x

C. (Fg)(x)

(X^2-7x+6)(x-6)

= x^3-13x^2+48x-36

D. (H/p)(x)

X/x-1 / 2x/x+4

X/x-1 / x+4/2x

= X^2+4x/2x^2-2x

3.

A. (F+g)(3)

X^2+1 + x-4

3^2+1 + 3-4

10 -1

= 9

B. (f-g)(0)

X^2+1 - x-4

0+1 -0-4

1-4

= -3

C. (Fg)(-k)

(X^2+1) (x-4)

(-k^2+1) (-k-4)

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D. (F/g)(k-2)

X^2+1 /x-4

K-2^2+1 / k-2 -2

= K^2-4k+5 / k-4

Step-by-step explanation:

8 0
3 years ago
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