What is the focal length of the parabola whose graph is shown? focus: (-3, 2.6) and directrix: (-0.6)

Answers

Answer 1

Answer: The distance from the focus to the directrix is twice the focal length. Using the distance formula, 2.6+(-0.6) = 3.2. Half of this value is the focal length. 3.2/2 = 1.6. Therefore, the focal length of the parabola with a focus of (-3,2.6) and directrix of -0.6 is 1.6.

Answer 2

Answer:

Final answer:

The focal length of a parabola is the distance from its focus to the directrix. In this case, the focal length is calculated to be 2.4 units.

Explanation:

In Mathematics, particularly in the study of conic sections, the focal length of a parabola is the distance from the focus to the directrix of the parabola. Given the focus as (-3, 2.6) and the directrix as (-0.6), we can calculate the focal length by using the formula for the distance between a point and a line in a plane, which is |x-x1|. |x-x1| is the absolute value of the difference between the x-coordinate of the focus and the equation of the directrix. Here, x1 is -3 (from the focus) and x is -0.6 (from the directrix). So, the focal length of the parabola is |-0.6 - (-3)| = |-0.6 + 3| = 2.4 units.

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