Question

If the parabola y² = 4ax passes through the point (2, 4), then the focus of parabola is ?
1. (1,1)
2. (0,1)
3. (2,0)
4. (0,0)

Answer 1

Correct Answer - Option 3 : (2,0)

Concept:

The focus of Parabola y2 = 4ax is (a, 0).

Calculation:

The equation of parabola is y2 = 4ax and it passes through (2, 4).

So this point satisfy the equation of parabola i.e x = 2 and y = 4 will satisfy the equation of parabola

⇒  42 = 4a × 2

⇒ 16 = 8a

⇒ a = 2

As we know that the focus of parabola y2 = 4ax is (a, 0)

So, the focus of the parabola is (2, 0)

Hence, option 3 is correct.