Find the distance between each pair of points. (7 1/2, -6) and (7 1/2, -2 1/2)
1 answer:
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Answer:
Step-by-step explanation:
If you plot this point and the directrix on a coordinate plane, you can see that the directrix is 1/4 of a unit below the vertex. Since, by nature, a parabola opens in the direction opposite the directrix and "hugs" the focus, this is a positive x-squared parabola (meaning it opens upwards). The formula for this type of a parabola is, in vertex form,
where p is distance (in units) between the vertex and the directrix and h and k are the coordinates of the vertex. For us, p = .25, h = 7, and k = -6. Filling in our formula:
Simplify the left side to
which simplifies, in its entirety, to
You can graph them on Desmos, then use this attachment to find out the classification.
In the first system, they're the same line and have infinitely many solutions, therefore the answer is consistent, dependent.
In the second system, they're parallel lines with no solution, therefore the answer is inconsistent.
In the third system, they intersect and they have one solution, therefore the answer is consistent, independent.
In the fourth system, they're the same line and have infinitely many solutions, therefore the answer is consistent, dependent.
In the first system, they're the same line and have infinitely many solutions, therefore the answer is consistent, dependent.
In the second system, they're parallel lines with no solution, therefore the answer is inconsistent.
In the third system, they intersect and they have one solution, therefore the answer is consistent, independent.
In the fourth system, they're the same line and have infinitely many solutions, therefore the answer is consistent, dependent.