Question

X^2 + y^2+ 4x- 2y = - 1

The equation of a circle in the x-y plane is shown above. What is the Radius of the Circle

2

3

4

9

Answer 1

r = 2

Explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² + 4x - 2y = - 1 ← rearrange the x and y terms together

x² + 4x + y² - 2y = - 1

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(2)x + 4 + y² + 2(- 1)y + 1 = - 1 + 4 + 1

(x + 2)² + (y - 1)² = 4 ← in standard form

with r² = 4 ⇒ r =
`√(4)` = 2