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AURORKA [14]
3 years ago
6

Derive the equation of the parabola with a focus at (_5, 5) and a directrix of y = -1.

Mathematics
2 answers:
timurjin [86]3 years ago
5 0
The answer is f(x) = one twelfth (x + 5)2 + 2, that is found when <span>focus and  directrix of a parabola's formula is applied. </span>
mars1129 [50]3 years ago
4 0

Answer: Option D is correct.

Step-by-step explanation:

Since we have given that

focus = (-5,5)

and a directrix y= -1

Since, equation of parabola in this case will be

(x-h)^2=4.a(y-k)

Now, here

y=k-a=-1\\\\\text { focus =(h,k+a)}\\\\\text{So,} k+a=5\\\\\text{ by solving these two equation , we get }\\\\a=3\text{ and } k=2

So equation will be

(x+5)^2=4\times 3(y-2)\\\\(x+5)^2=12(y-3)\\\\y=\frac{1}{12}(x+5)^2+2

So, option D is correct .

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