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Consider a circle whose equation is
[tex] {x}^{2} + {y}^{2} - 2x - 8 = 0.[/tex]
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
[tex] {x}^{2} + {y}^{2} = 9.[/tex]

(B) The standard form of the equation is
[tex] {(x - 1)}^{2} + {y}^{2} = 3.[/tex]

(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.​

Respuesta :

amna04352

Answer:

A, D, E

Step-by-step 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

joseaaronlara

Answer:

The answer to your question is below

Step-by-step 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.

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