Question

Select the correct answer from each drop-down menu.

Answer 1

The correct options regarding the circle with endpoints of the longest chord at (4, 5.5) and (4, 10.5) are:

• The center is (4,8).

• The radius is of 2.5 units.

• $(x - 4)^2 + (y - 8)^2 = 6.25$

What is the equation of a circle?

The equation of a circle of center $(x_0, y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

The center is the midpoint of the chords, hence:

• $x_0 = \frac{4 + 4}{2} = 4$.

• $y_0 = \frac{5.5 + 10.5}{2} = 8$.

The radius is half the distance between the chords, hence:

$r = 0.5\sqrt{(4-4)^2 + (10.5 - 5.5)^2} = 0.5 = 2.5$.

Hence the equation is:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

$(x - 4)^2 + (y - 8)^2 = 2.5^2$

$(x - 4)^2 + (y - 8)^2 = 6.25$

More can be learned about the equation of a circle at brainly.com/question/24307696

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