$T h e e q u a t i o n o f c i r c u m - c i r c l e o f a Δ A B C i s x^{2} + y^{2} + 3 x + y - 6 = 0. I f A = (1, - 2), B (- 3, 2) a n d t h e v e r t e x C v a r i e s t h e n t h e l o c u s o f o r t h o - c e n t r e o f Δ A B C i s a$

Straight line

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Circle

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Parabola

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Ellipse

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Solution

The correct option is B
Circle

Let c = (x,y,) and ortho centre = (x, y) since A, B and C are points on the circle we have centroid $G = (\frac{\sum x}{3}, \frac{\sum y}{3}) (x, y) = (x_{1} - 2, y_{1})$
$\Rightarrow (x, y_{1}) = (x + 2, y)$ Which lies on the given circle $\Rightarrow$ locus is a circle

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