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x² + y² + 4x – 2y = -1
The equation of a circle in the xy-plane is shown above. What is the radius of the circle?

A 2
B 3
C 4
D 5

please answer this..
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Sagot :

IHATEnonsenseidn

Answer:

D. 5

Step-by-step explanation:

I really hate nonsense

JesssaGeumidn

[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]

  • A 2

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]

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