Question

The circumcentre of the triangle formed by the lines $x^2-y^2=0$ and $y-5=0$ is

• A. $(5,0)$
• B. $(0,5)$
• C. $(0,0)$
• D. $(5,5)$

Answer 1

Answer: (B)

$(0,5)$

$x^2-y^2=0$

$y=x$ and
$y=-x$

And $y=5$

By symmetry
circumcentre lie on y-axis

i.e. $P(0,y)$ is circumcentre of $\Delta OAB$

$\therefore$ distance of verties from p is same

$\therefore PO=PA$

$\therefore y^2=25+(y-5{)}^2$

$y^2=25+y^2-10y+25$

$\Rightarrow 10y=50$

$\Rightarrow y=5$

$\therefore P(0,5)$ is circumcentre of $\Delta OAB$