Question

The circle passing through $(t,1),(1,t)$ and $(t,t)$ for all values of $t$ also passes through

• A. $(0,0)$
• B. $(1,1)$
• C. $(1,-1)$
• D. $(-1,-1)$

Answer 1

The correct option is B $(1,1)$

The general equation of circle is

$(x-h{)}^2+(y-k{)}^2=r^2,$ where h and k are the

coordinates of center of circle.

if It passes through $(1,t)$ so $(1-h{)}^2+(t-k{)}^2=r^2$ __ (1)

if It passes through $(t,t)$ so $(t-h{)}^2+(t-k{)}^2=r^2$ __ (2)

if It passes through $(t,1)$ so $(t-h{)}^2+(1-k{)}^2=r^2$ __ (3)

on solving eq (1) & (2)

$1-h=t-h\Rightarrow t=1$

It t = 1, then the circle passes through (1,1).