Question

A parabola is represented by the equation x2 = 4y.

What are the coordinates of the focus of the parabola?

(0,4)
(0,1)
(1,0)
(4,0)

Answer 1

Answer: The answer is (B) (0, 1).

Explanation: We are given to find the co-ordinates of the focus of the parabola represented by the following equation:

`x^2=4y.~~~~~~~~~~~~~~~(i)`

We know that the standard form of a parabola is given by

`(x-h^)2=4p(y-k),~~~~~~~~~~~~~~~~(ii)`

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

In standard form, the parabola (i) can be written as

`x^2=4y\\\\\Rightarrow (x-0)^2=4* 1(y-0)^2.`

Comparing it with the general form (ii) of a parabola, we have

`h=0,~k=0,~p=1.`

Therefore, the co-ordinates of the focus are

(h, k + p) = (0, 0 + 1) = (0, 1).

Thus, (B) is the correct option.

Answer 2

The equation of the parabola is x^2 = 4y
The graph of this parabola is curved upwards with the vertex at the origin. The general formula of a parabola is
x^2 = 4ay
So
4a = 4
a = 1
Therefore, the focus of the parabola is
(0,1)