Question

which is the focus of a parabola with equation y² = 4x? (-1, 0) (0, -1) (0, 1) (1, 0)

Explanation:

Step1: Recall parabola standard - form

The standard form of a parabola opening to the right or left is $y^{2}=4px$. Comparing $y^{2}=4x$ with $y^{2}=4px$, we get $4p = 4$.

Step2: Solve for $p$

Dividing both sides of $4p = 4$ by 4, we have $p=\frac{4}{4}=1$.

Step3: Find the focus

For a parabola of the form $y^{2}=4px$ opening to the right (since $p>0$), the focus is at the point $(p,0)$. Substituting $p = 1$, the focus is $(1,0)$.

Answer:

$(1,0)$