The parabola has a focus at (−3, 0) and directrix y = 3. what is the correct equation for the parabola? x2 = −12y x2 = 3y y2 = 3x y2 = −12x

The directrix is a straight line that is found at the back of the opening of the parabola with a distance equal to its focal length. So, if the directrix is y = 3, that means that the focal length is 3 and the opening is downwards. The general equation for a parabola opening downwards is:

(x - h)² = -4a(y - k)
where a is the focal length and (h,k) is the vertex

We know a = 3. Now, since focus is at (-3,0) and directrix is at y=3, the middle of -3 and 3 is 0. So, the vertex is at the origin. Therefore, the equation would be:

x² = -12y

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c