Question

The equation of a parabola is 1/32 (y−2)2=x−1 .

Answer 1

The given equation of parabola is

$\frac{1}{32} (y-2)^2 = x-1$

Which can also be written as

$x = \frac{1}{32} (y-2)^2 +1$

Here vertex (h,k) is (1,2)

And value of a is

$a = \frac{1}{32}$

Formula of focus is

$(h+ \frac{1}{4a} , k)$

Substituting the values of h,k and a, we will get

$(1+ \frac{1}{4*(1/32) } , 2} = (1+ 8,2) = (9,2)$

Therefore the correct option is the last option .

Answer 2

Answer:  The correct option is (D) (9, 2).

Step-by-step explanation:  We are given to find the co-ordinates of the focus for the following parabola:

$\dfrac{1}{32}(y-2)^2=x-1~~~~~~~~~~~~~~~~~~~~(i)$

We know that the standard form equation of a parabola is

$(y-k)^2=4p(x-h),$

where the co-ordinates of the focus are (h+p, k).

From equation (i), we have

$\dfrac{1}{32}(y-2)^2=x-1\\\\\\\Rightarrow (y-2)^2=32(x-1)\\\\\Rightarrow (y-2)^2=4\times 8(x-1).$

Comparing the above equation with the standard form equation of the parabola, we get

h = 1, k = 2, and p = 8.

Therefore, the co-ordinates of the focus are

$(h+p,k)=(1+8,2)=(9,2).$  

Thus, option (D) is CORRECT.