I don't know how to solve for the Area and Circumference but I know how to solve for the equation but I just wanted to make sure... Any help and explanations would be appreciated :)
Problem: A circle is centered at (2, 1) and tangent to the line x + y=0. Find the general equation of the circle, the area and circumference...
Let the radius of the circle be r. Then, its equation is $(x – 2)^2 + (y – 1)^2 = r^2$ … (1)
It cuts the line $x + y = 0$ …. (2)
Eliminate y from (1) and (2) to obtain a quadratic equation in x (with the unknown r) … (3)
(2) is tangent to (1) means (3) has only one root. Therefore, solving ⊿ = 0, we get the value of $r^2$.
Then, re-write (1).