[tex]\large{x² + y² + 4x \: – \: 2y = -1}[/tex]
The equation of a circle in the xy-plane is shown above. What is the radius of the circle?
[tex] \\ [/tex]
B 3
C 4
D 5
[tex] \\ [/tex]
Explanation:
In the standard form of the equation of a circle, which is [tex]\textrm{(x-h)²}[/tex] + [tex]\textrm{(y-k)² = r² }[/tex], where [tex]\textrm{(h,k)}[/tex] is the center of the circle and [tex]\textrm{r}[/tex] is the radius. Now we will need to rewrite this/the equation into standard form to easily we find the radius.
Solve:
[tex] \large \begin{array}{l}{ x² + 4x + y² - 2y = -1} \\ (x+2)² - 4+ (y-1)² -1 = -1 \\ (x+2)² + (y-1)² = -1 + 1 + 4 \\ (x+2)² + (y-1)² = \blue{4} \\ \sqrt{ \blue4} = {\boxed{ \bold\green{{2}}}} \end{array}[/tex]
Now we see that [tex]r² = 4[/tex], so the radius is [tex] \sqrt{ \blue4} = \underline\green{2}[/tex]
[tex] \\ [/tex]
Hope Its Helps!
Aral Mabuti!
