Question

What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0?

Answer 1

2 units

Explanation:

The given equation of the circle is:

`x^(2) + y^(2)+8x-6y+21=0`

The general equation of the circle is:

`x^(2) + y^(2)+2gx+2fy+c=0`

Comparing the given equation with the general equation we can say:

g = 4

f = -3

c = 21

The formula for radius of the circle is:

`radius=\sqrt{g^(2) +f^(2) -c }`

Using these values of the given circle, we get:

`radius=\sqrt{(4)^(2)+(-3)^(2)-21}\\\\radius=√(4)\\\\radius=2`

Therefore, the length of radius of the given circle is 2.