Write an equation for a parabola with endpoints of the latus rectum at (-2, 3) and (-2, 15) and the directrix at x = 4.

Given:

The endpoints of the latus rectum at (-2, 3) and (-2, 15).

The directrix at x = 4.

To find:

The equation of the parabola.

Solution:

The equation of the parabola is:

                  ...(1)

Where, is directrix and are the end point of the latus rectum.

The directrix at x = 4. So,

              ...(i)

The endpoints of the latus rectum at (-2, 3) and (-2, 15). So,

Now,

             ...(ii)

             ...(iii)

          ...(iv)

Adding (i) and (ii), we get

Putting in (i), we get

Putting in (iii), we get

Putting in (1), we get

Therefore, the required equation of the parabola is .

idk

step-by-step explanation: