Question

Consider a circle whose equation is


`{x}^(2) + {y}^(2) - 2x - 8 = 0.`
Which statements are true? Select three options.

(A) The radius of this circle is the same as the radius of the circle whose equation is

`{x}^(2) + {y}^(2) = 9.`

(B) The standard form of the equation is

`{(x - 1)}^(2) + {y}^(2) = 3.`

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

(D) The radius of the circle is 3 units.

(E) The center of the circle lies on the x-axis.​

Answer 1

A, D, E

Explanation:

x² + y² - 2x - 8 = 0

Centre is (0,1)

0² + 1² - r² = -8

r² = 9

r = 3

Completed square form:

(x-1)² + y² = 3²

(x-1)² + y² = 9

Answer 2

The answer to your question is below

Explanation:

Data

x² + y² - 2x - 8 = 0

- Find the radius and the center

x² - 2x + y² = 8

x² - 2x + 1 + y² = 8 + 1

(x - 1)² + y² = 9

- Center = (1, 0) Radius = 3

a) True, both circles have the same radius (3)

b) False, the standard equation is (x - 1)² + y² = 9

c) False, the center of the circle lies on the x-axis

d) True, the radius of the circle is 3 units

e) True, the center of the circle lies on the x-axis.