Question

If the radius of the circle x² + y2 - 4x - 6y - k = 0 is

4 units, find the value of k.

​

Answer 1

Answer: 3

Explanation:

Given

The equation of the circle is
`x^2+y^2-4x-6y-k=0`

Using completing the square method

`\Rightarrow x^2+y^2-4x-6y+4-4+9-9-k=0\\\Rightarrow \left( x^2-4x+4\right)+\left( y^2-6y+9\right)-\left( k+4+9\right)=0\\\Rightarrow \left( x-2\right)^2+\left( y-3\right)^2=\left( k+13\right)`

on comparing with standard form,
`r^2=k+13`

Insert the value of r

`\Rightarrow 4^2=k+13\\\Rightarrow k=16-13\\\Rightarrow k=3`