The x- and y-coordinates of the focus of a parabola are (1,3) and the directrix is y=-5 . a second parabola is a translation 1 unit right and 2 units up of the first parabola. write an equation of the second parabola.

The equation of the second parabola is

Step-by-step explanation:

We know that the focus of the first parabola is (1,3) and the directrix is y = -5. We also know that the second parabola is a translation 1 unit right and 2 units up of the first parabola.

We can use the focus of the first parabola to find the focus of the second parabola (1+1, 3+2) = (2, 5) and the directrix of the second parabola is moved 2 units up. The equation of the directrix of the second parabola is y = -3.

To find the parabola equation we start by assuming a general point on the parabola (x,y).

Next, with the help of the distance formula we find that the distance between (x,y) and the focus.

The distance between (x,y) and the directrix y = -3 is

On the parabola, these distances are equal:

The equation of the second parabola is

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step-by-step explanation: