Circle C₁ has equation $x^{2} + y^{2} - 6x - 2y - 26 = 0$ - Scottish Highers Maths - Question 3 - 2022

We start with the equation of circle C₁:

$x^{2} + y^{2} - 6x - 2y - 26 = 0$

To find the radius, we need to rewrite this equation in standard form. We will complete the square for both $x$ and $y$ terms.

1. Rearranging gives:
   $x^{2} - 6x + y^{2} - 2y = 26$

2. Completing the square for $x$:
   $x^{2} - 6x = (x - 3)^{2} - 9$

3. Completing the square for $y$:
   $y^{2} - 2y = (y - 1)^{2} - 1$

Putting these together, we have:

$(x - 3)^{2} - 9 + (y - 1)^{2} - 1 = 26$

Simplifying gives:

$(x - 3)^{2} + (y - 1)^{2} = 36$

Thus, the radius of circle C₁ is given by:

$r_{1} = ext{√}(36) = 6$