If the radius of the circle passing through the origin and touching the line x + y = 2 at 1,1 is r units, then the value of 3 2 r is

Question

If the radius of the circle passing through the origin and touching the line x + y = 2 at 1,1 is r units, then the value of 3 2 r is,

MARKS App · Accepted Answer

Family of circles touching the given line at the given point is

{(x - 1)}^{2} + {(y - 1)}^{2} + λ (x + y - 2) = 0

It passes through

(0,0)

, hence

2 - 2 λ = 0 \Rightarrow λ = 1

So, the equation of the circle is

x^{2} + y^{2} - x - y = 0

Radius

= \frac{1}{\sqrt{2}}