Question

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.



The radius of the circle is 3 units.

The center of the circle lies on the x-axis.

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

The standard form of the equation is (x – 1)² + y² = 3.

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

Answer 1

Answer:

The first, second, and fifth statements are correct.

Step-by-step explanation:

We are given a circle with the equation:

$x^2+y^2-2x-8=0$

And we want to select the statements that are true.

First, we can convert the equation into standard form. We can group each variable:

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

And complete the square for the first term:

$(x^2-2x+1)+(y^2)=8+1$

Factor and simplify:

$(x-1)^2+y^2=9$

We can rewrite our equation as:

$(x-(1))^2+(y-(0))^2=(3)^2$

So, this tells us that we have a circle centered on (1, 0) with a radius of 3 units.

In this case, the first statement, second statement (the point (1,0) is on the x-axis), and fifth statements are correct (the square root of 9 is also 3).

Answer 2

Answer:

The first, second, and fifth statements are correct.

Step-by-step explanation:

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