The table shows two sequences of numbers.
2 answers:
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The geometrical relationships between the straight lines AB and CD is that they are parallel to each other
<h3>How to determine the relationship</h3>It is important to note the following;
- A drawn from the origin and passes through point A (a , b), then the equation of OA = ax + by
- If a line is drawn from the origin and passes through point B (c , d), then the equation of OB = cx + dy
We find the equation of AB by subtracting OB from OA, thus AB = (c - a)x + (d - b)y
The slope of line AB =
⇒ OA= 2 x + 9 y
⇒ OA = 4 x + 8 y
⇒AB = OB - OA
⇒AB = (4 x + 8 y) - (2 x + 9 y)
⇒ AB = 4 x + 8 y - 2 x - 9 y
Collect like terms
⇒ AB = (4 x - 2 x) + (8 y - 9 y)
⇒AB = 2 x + -y
⇒ AB = 2 x - y
⇒ Coefficient of x = 2
⇒ Coefficient of y = -1
⇒ The slope of ab = = 2
For CD
⇒ CD = 4 x - 2 y
⇒Coefficient of x = -4
⇒ Coefficient of y = -2
⇒The slope of cd = = 2
Note that Parallel lines have same slopes
And Slope of ab = slope of cd
AB // CD
Therefore, the geometrical relationships between the straight lines AB and CD is that they are parallel to each other
Learn more about parallel lines here:
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Answer:
the length of the conjugate axis is 16
Step-by-step explanation:
We know that the general equation of a hyperbola with transverse horizontal axis has the form:
Where the point (h, k) are the coordinates of the center of the ellipse
2a is the length of the transverse horizontal axis
2b is the length of the conjugate axis
In this case the equation of the ellipse is:
Then
Finally the length of the conjugate axis is 16