Question

Consider a circle whose equation is x + y - 2x - 8=0. Which statements are true? Select three options
The radius of the circle is 3 units
The center of the circle hes on the x-axis
The center of the orde hes on the y-axis
The standard form of the equation is (x-1)' + y = 3
The radius of this circle is the same as the radius of the circle whose equation is x + y = 9​

Answer 1

Answer:

The standard form of the equation is

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

Step-by-step explanation:

The given circle has equation:

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

We regroup similar terms to obtain:

${x}^{2} -2x + {y}^{2} = 8$

We now complete the square to obtain:

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

${(x - 1)}^{2} + {(y - 0)}^{2} = 9$

Or

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

This is now of the form:

${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

which is referred to as the standard form equation of the circle: