r is perpendicular to 2
x -
y + 1 = 0. Thus, equation of
r is
$x + 2y = 2 + 2(5)$
$x + 2y = 12$
Another way to solve for the equation of r
The center (h, k) is the point of intersection of r and x + y = 9.
From x + 2y = 12 and x + 2 = 9
$x = 6$
$y = 3$
Thus, center (h, k) = (6, 3)
Length of radius r = distance from line 2x - y + 1 = 0 to center (6, 3)
$r = \dfrac{ax_1 + by_1 + c}{\pm \sqrt{a^2 + b^2}} = \dfrac{2(6) - 3 + 1}{\sqrt{2^2 + 1^2}}$
$r = 2\sqrt{5} ~ \text{units}$
Equation of the required circle
$(x - h)^2 + (y - k)^2 = r^2$
$(x - 6)^2 + (y - 3)^2 = (2\sqrt{5})^2$
$(x^2 - 12x + 36) + (y^2 - 6y + 9) = 20$
$x^2 + y^2 - 12x - 6y + 25 = 0$ answer
