Given:
The given equation is
To find:
The vertex, focus, and directrix.
Solution:
The equation of a parabola is
...(i)
where, (h,k) is vertex, and directrix is
We have,
It can be written as
...(ii)
On comparing (i) and (ii), we get
Vertex of the parabola is (2,3).
Therefore, the focus of the parabola is .
Directrix of the parabola is
Therefore, the directrix of the parabola is .
We must determine the y-intercept, b using the slope and point provided.
Now that we know the y-intercept, b, we can create the equation of this line: <em>y = -3x + 1</em>.
Answer:
5, 6, 7, 8, 9, 10, 11, 12, and 13.
Step-by-step explanation:
We can use the triangle inequality. By the triangle inequality, the sum of any two sides of a triangle must be greater than the remaining side.
In other words, the sum of the two shorter sides must be greater than the longest side.
We know that PQ is 5 and PR is 9.
For the first case, let's say that neither PQ nor PR is the longest side. Instead, QR is the longest side. Then their sum must be greater than QR. Thus:
However, for the second case, let's say that QR is not the longest side. In this case, PR will be the longest side. Therefore, QR plus PQ must be greater than PR:
Thus, we have a compound inequality:
Therefore, the possible whole-number lengths of QR are:
5, 6, 7, 8, 9, 10, 11, 12, and 13.