2. what is the center and the radius of a circle given by the equation x2 + y2 + 4x - 10y + 20 = 0? ,5) and r=square root of 25 b.(2,-5) and r=square root of 20 ,5) and r=3 d.(2,-5) and r=3

C

Step-by-step 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 - 10y + 20 = 0

Collect x and y terms and subtract 20 from both sides. that is

x² + 4x + y² - 10y = - 20

To obtain standard form use the method of completing the square

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

x² + 2(2)x + 4 + y² + 2(- 5)y + 25 = - 20 + 4 + 25

(x + 2)² + (y - 5)² = 9 ← in standard form

with centre = (- 2, 5) and r = = 3 → C

step-by-step explanation:

sry but any answer choices