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daser333 [38]
3 years ago
7

Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. f(x) = −one eighth (x − 2)2 + 6 f(x) = one

eighth (x − 2)2 + 6 f(x) = −one eighth (x + 2)2 + 8 f(x) = one eighth (x + 2)2 + 8
Mathematics
2 answers:
Basile [38]3 years ago
6 0

Answer:  f(x) = −one eighth (x − 2)2 + 6


vfiekz [6]3 years ago
3 0

Answer:

A

Step-by-step explanation:

For any point (x, y ) on the parabola the focus and directrix are equidistant

Using the distance formula

\sqrt{(x-2)^2+(y-4)^2} = | y - 8 |

Squaring both sides gives

(x - 2)² + (y - 4)² = (y - 8)²

(x - 2)² + y² - 8y + 16 = y² - 16y + 64 ( rearrange and simplify )

(x - 2)² = - 8y + 48

8y = - (x - 2)² + 48

y = - \frac{1}{8}(x - 2)² + 6 → A


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Given parameters;

  Let us solve this problem step by step;

Let us represent Simon's money by S

Kande's money by K

  • Simon has more money than Kande

               S > K

  •  if Simon gave Kande K20, they would have the same amount;

 if Simon gives $20, his money will be  S - 20 lesser;

      When Kande receives $20, his money will increase to K + 20

                     S - 20  = K + 20   ------ (i)

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          if Kande gave Simon $22, his money will be K - 22

    Simon's money, S + 22;

                  S + 22  = 2(K - 22)    ------ (ii)

Now we have set up two equations, let us solve;

         S - 20  = K + 20  ---- i

         S + 22  = 2(K - 22)  ;       S + 22  = 2K - 44  ---- ii

So,      S - 20  = K + 20

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subtract both equations;

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                   -42  = -k + 64

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Using equation i, let us find S;

            S - 20 = K + 20

             S - 20  = 106 + 20

              S = 106 + 20 + 20  = 146

Therefore, Kande has $106 and Simon has $146

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