What is the equation of the directrix of the parabola given by the equation y2 = -24x?
1 answer:
Hello!
The directrix of a parabola is a fixed line used in describing a curve or surface.
The standard form a parabola is 4p(x - h) = (y - k)². In this equation, h, k is the vertex, and p is the focal point.
To find the standard form, first, we would find p.
Since the equation given, y² = -24x, has a vertex at (0, 0), h, k would be zero. In this case, we can find p now.
4p = -24 (divide both sides by 4)
p = -6
4(-6)(x - 0) = (y - 0)² which can be simplified to: 4(-6)(x) = y².
Looking at the graph of the parabola, it is symmetric around the x-axis, so therefore, the directrix is a line parallel to the y-axis. To find the directrix, use the formula: x = 0 - p, and we know that p = -6.
x = 0 - (-6)
x = 6
Therefore, the directrix of the parabola is choice D, x = 6.
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Answer:
The length of the base is 11 meters.
Step-by-step explanation:
The diagram of the triangle is not shown; However, the given details are enough to solve this question.
Given
<em>Shape: Triangle</em>
<em>Represent the height with h and the base with b</em>
Required
Find the length of the base
The area of a triangle is calculated as thus;
Substitute 22 for Area and 3 + 2h for b
The formula becomes
Multiply both sides by 2
Open the bracket
Subtract 44 from both sides
Rearrange
At this point, we have a quadratic equation; which is solved as follows:
Split the above
Solve the above linear equations separately
Add 4 to both sides
---- <em>First value of h</em>
Subtract 11 from both sides
Divide both sides by 2
<em> ------ Second value of h</em>
Since height can be negative, we'll discard
Hence, the usable value of height is
Recall that
Substitute 4 for h
Hence, the length of the base is 11 meters