The line x=y touches a circle at the point (1,1).

Question

The line $x=y$ touches a circle at the point $(1,1)$. If the circle also passes through the point $(1,-3)$, then its radius is:

Accepted Answer

Equation of circle = (x -- 1)2 + (y --1)2 + $$\lambda (y -- x) = 0

Which passes through (1, --3)

So, 0 + 16 + \[\lambda (--3 -- 1) = 0

16 + \[\lambda (--4) = 0

\[ \therefore $$ $$\lambda $$ = 4

Now equation of circle

(x -- 1)2 + (y -- 1)2 + 4y -- 4x = 0

$$ \Rightarrow $$ x2 + y2 -- 6x + 2y + 2 = 0

radius = $$\sqrt {9 + 1 - 2}  = 2\sqrt 2 $$

Solutions · 1