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What is the radius of a circle whose equation is x2+y2+8x-6y+21=0?
O 2 units
O 3 units
4 units
ОО
O 5 units

Sagot :

razz25

Answer:

the correct answe is 2 cm

Step-by-step explanation:

if u need process I have...

oladayoademosu

The radius of the circle whose equation is x² + y² + 8x - 6y + 21 = 0 is 2 units

Radius of a circle

Since the equation of the circle is x² + y² + 8x - 6y + 21 = 0, to find the radius, we complete the square in the terms x and y and convert it to the form (x - a)² + (y - b)² = r²  (1) which is the standard equation of a circle.

So, x² + y² + 8x - 6y + 21 = 0

x² + 8x + y² - 6y + 21 = 0

x² + 8x + (8/2)² - (8/2)² + y² - 6y + (-6/2)²  + (-6/2)² + 21 = 0

x² + 8x + 4² - 4² + y² - 6y + (-3)²  - (-3)² + 21 = 0

(x + 4)² - 4² + (y - 3)²  - (-3)² + 21 = 0

(x + 4)² - 16 + (y - 3)²  - 9 + 21 = 0

(x + 4)² + (y - 3)² - 16 - 9 + 21 = 0

(x + 4)² + (y - 3)² - 4 = 0

(x + 4)² + (y - 3)² = 4  (2)

Comapring (1) and (2), r² = 4

So, r = √4

r = 2

So, the radius of the circle whose equation is x² + y² + 8x - 6y + 21 = 0 is 2 units

Learn more about equation of a circle here:

https://brainly.com/question/24810873

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