Consider a circle whose equation is x^2 + y^2 – 2x – 8 = 0. which statements are true? check all that apply.

a. the radius of the circle is 3 units.
b. the center of the circle lies on the x-axis.
c. the center of the circle lies on the y-axis.
d. the standard form of the equation is (x – 1)² + y² = 3.
e. the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

 The correct options are

A. The radius of the circle is 3 units.

C. The center of the circle lies on the y-axis.

E. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:  The given equation of the circle is

We are given to select the TRUE statements from the given options.

The standard form of a circle with radius r units and center (h, k) is given by

From equation (i), we have

comparing the above equation with the standard equation of a circle, we get

center, (h, k) = (0, 1)  and  radius, r = 3 units.

since the x co-ordinate of the center (0, 1) is 0, so it lies on the Y-axis.

Now, we have

So, the radius of this circle is 3 units.

That is, the radius of the given circle is same as the radius of the circle whose equation is

Thus, the standard equation of the given circle is

the center lies on the Y-axis, the radius is 3 units and the radius of the given circle is same as the radius of the circle whose equation is

Options (A),(C) and (E) are correct.

21

step-by-step explanation:

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no

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