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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let a circle of radius $4$ pass through the origin $O$, the point $A(-\sqrt{3}a,0)$ and $B(0,-\sqrt{2}b)$, where $a$ and $b$ are real parameters and $ab\ne0$. Then the locus of centroid of $\triangle OAB$ is a circle of radius:
Solution
$AB=8$
$3a^2+2b^2=64$
Centroid $G(h,k)$
$h=\frac{-\sqrt{3}a}{3},\quad k=\frac{-\sqrt{2}b}{3}$
$a=-\sqrt{3}h,\quad b=-\frac{3k}{\sqrt{2}}$
Substitute
$9h^2+9k^2=64$
$x^2+y^2=\frac{64}{9}$
$\Rightarrow r=\frac{8}{3}$
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