Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.

The standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2 is .

Step-by-step explanation:

The standard form of the parabola is

The general form of the parabola is

        ..... (1)

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

It is given that the parabola with a focus at (0, 2) and a directrix at y = -2. It means

      .... (2)

      .... (3)

On solving (2) and (3), we get

Substitute h=0, k=0 and p=2 in equation (1).

Divide both sides by 8.

Therefore the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2 is .

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step-by-step explanation: