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2 answers:
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Answer:
Step-by-step explanation:
Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form
The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.
Filling in the equation with a vertex of (0, 0) which is our h and k respectively:
which simplifies to
and multiplying both sides by -1:
. This is not standard form, but it matches what your equation is in the choices. So to sum up:
The focus is located at (0, -3) and the first choice is true.
The parabola opens upside down and the second choice is not true.
The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.
We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.
So the fifth choice is not true.
Surface area of sphere is
Step-by-step explanation:
We need to find the surface area of the sphere while we are given volume of sphere = 972π
The formula used to find surface area is:
We need to find radius of sphere
We are given Volume = 972π, using this volume we can find radius of sphere
The formula used to find volume is:
Putting values and finding r
Taking cube root on both sides
So, Radius of sphere r=9
Now finding surface area:
So, surface area of sphere is
Keywords: Surface area of sphere
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