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

What are the coordinates of the focus?


(1, 10)

(1, −6)

(−7, 2)

(9, 2)

Respuesta :

Riia

The given equation of parabola is

[tex] \frac{1}{32} (y-2)^2 = x-1 [/tex]

Which can also be written as

[tex] x = \frac{1}{32} (y-2)^2 +1 [/tex]

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

And value of a is

[tex] a = \frac{1}{32} [/tex]

Formula of focus is

[tex] (h+ \frac{1}{4a} , k) [/tex]

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

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

Therefore the correct option is the last option .

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:

[tex]\dfrac{1}{32}(y-2)^2=x-1~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that the standard form equation of a parabola is

[tex](y-k)^2=4p(x-h),[/tex]

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

From equation (i), we have

[tex]\dfrac{1}{32}(y-2)^2=x-1\\\\\\\Rightarrow (y-2)^2=32(x-1)\\\\\Rightarrow (y-2)^2=4\times 8(x-1).[/tex]

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

[tex](h+p,k)=(1+8,2)=(9,2).[/tex]  

Thus, option (D) is CORRECT.

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