Question

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

f(x) = _one twelfth (x _ 5)2 + 2
f(x) = one twelfth (x _ 5)2 + 2
f(x) = _one twelfth (x + 5)2 + 2
f(x) = one twelfth (x + 5)2 + 2

Answer 1

Answer: Option D is correct.

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* 3(y-2)\\\\(x+5)^2=12(y-3)\\\\y=(1)/(12)(x+5)^2+2`

So, option D is correct .