Answer:
Part A)
5th and 6th Choices
Part B)
Step-by-step explanation:
We are given a parabola with focus at (2, -4) and the directrix given by <em>y</em> = -6.
Part A)
Since our directrix is an equation of <em>y</em>, the distance from any point (x, y) on the parabola to the directrix will simply be the absolute value of the difference of the y-values. Hence:
Again, we will use the distance formula. Let the point (x, y) be (x₂, y₂) and our focus (2, -4) be (x₁, y₁). Then by the distance formula:
Hence, our answers are the 5th and 6th choices.
Part B)
By definition, any point (x, y) on the parabola is equidistant to the focus and the directrix. Hence:
Square both sides. We may remove the absolute value as anything squared yields a positive. Hence:
Square:
Rearrange:
Combine like terms:
Divide both sides by 4. Hence, our equation is: