If the radius of the circle $$x^2+y^2-6x+8y+c=0$$​ is 6, then the value of $$c$$​ is:

Correct option is B

Given:

The equation of the circle is:

​$$x^2 + y^2 - 6x + 8y + c = 0$$​​

The radius of the circle is 6.

Concept Used:

The general equation of a circle is:

​$$x^2 + y^2 + 2gx + 2fy + c = 0$$​​

where:

Centre =(−g,−f)

Radius =$$\sqrt{g^2 + f^2 - c}$$​​

Solution:

Comparing with the given equation:

2g = −6=>g = −3 , 2f = 8=> f = 4

Using the radius formula:

​$$\sqrt{g^2 + f^2 - c} = 6$$​​

​$$\sqrt{(-3)^2 + (4)^2 - c} = 6$$​​

​$$\sqrt{9 + 16 - c} = 6$$

$$\sqrt{25-c}=6$$​​​

25−c=36

c = −11

Option (B) is right.