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Nadusha1986 [10]
3 years ago
14

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

Mathematics
2 answers:
Andru [333]3 years ago
6 0

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 .

adelina 88 [10]3 years ago
4 0

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.

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