Aspotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x^2=4y around its axis of symmetry (assume that x and y are in units of inches). in order to have the brightest, most concentrated light beam, how far from the vertex should the bulb be placed? express your answer as a fraction or a decimal rounded to two decimal places.

  1.00 inches

Step-by-step explanation:

The distance from vertex to focus is "p" in the quadratic equation ...

  x^2 = 4py

In the given equation, p=1. Since units are inches, ...

the bulb should be placed 1.00 inches from the vertex.

linear pair postulates

the answer is (-8,-5)

step-by-step explanation:

the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)