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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let PQ and MN be two straight lines touching the circle $x^2 + y^2 - 4x - 6y - 3 = 0$ at the points $A$ and $B$ respectively. Let $O$ be the centre of the circle and $\angle AOB = \pi/3$. Then the locus of the point of intersection of the lines PQ and MN is:
Solution
Given circle
$x^2 + y^2 - 4x - 6y - 3 = 0$
$C(2,3)$ & $r = 4$
$\cos 30^\circ = \frac{r}{OR} = \frac{4}{OR}$
$\Rightarrow OR = \frac{8}{\sqrt{3}}$
Now
$OR^2 = (h - 2)^2 + (k - 3)^2$
$\Rightarrow 3(x^2 + y^2) - 12x - 18y - 25 = 0$
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