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  4. P is a variable point of the line L=0. Tangents are drawn to the circle x2+y2=4 from P to touch it at Q and R. The parallelogram PQSR is completed. If L ≡ 2 x+y-6=0, then the locus of circumcetre of triangle P Q R is -

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Q. $P$ is a variable point of the line $L=0$. Tangents are drawn to the circle $x^2+y^2=4$ from $P$ to touch it at $Q$ and $R$. The parallelogram PQSR is completed.
If $L \equiv 2 x+y-6=0$, then the locus of circumcetre of $\triangle P Q R$ is -

Conic Sections

Solution:

Parallelogram PQSR is a rhombus
Let circumcentre of $\triangle PQR$ is $(h, k)$
image
which is the middle point of $CP$
$\therefore P$ becomes $(2 h , 2 k )$ which satisfies the line $2 x+y-6=0$
$\therefore 2(2 h )+2 k -6=0$
$\therefore$ locus is $2 x+y-3=0$