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  • The equation of circumcircle of a   is <img alt="\mathrm{x}^2+\m

The equation of circumcircle of a \triangle \mathrm{ABC}  is \mathrm{x}^2+\mathrm{y}^2+3 \mathrm{x}+\mathrm{y}-6=0. If \mathrm{A}=(1,-2), \mathrm{B}=(-3,2)  and the vertex C varies then the locus of orthocenter of \mathrm{\triangle A B C}  is a
 

Option: 1

 Straight line
 


Option: 2

Circle
 


Option: 3

 Parabola
 


Option: 4

 Ellipse
 


Answers (1)

best_answer

Equation of circumcircle is \mathrm{\left(x+\frac{3}{2}\right)^2+\left(y+\frac{1}{2}\right)^2=\frac{17}{2} }
 

\begin{aligned} & \mathrm{C}=\left(-\frac{3}{2}+\sqrt{\frac{17}{2}} \cos \theta,-\frac{1}{2}+\sqrt{\frac{17}{2}} \sin \theta\right) \\ & \text { Circum centre of } \triangle \mathrm{ABC} \text { is }\left(-\frac{3}{2},-\frac{1}{2}\right) \end{aligned}
is \mathrm{\left(-\frac{3}{2},-\frac{1}{2}\right)}
Circum centre of \triangle \mathrm{ABC} \ is \ \left(-\frac{3}{2}, \frac{1}{2}\right)
Centroid can be obtained.

In a triangle centroid, circum centre and ortho centre are collinear.

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Anam Khan

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