If $\mathrm{P}(6,1)$ be the orthocentre of the triangle whose vertices are $\mathrm{A}(5,-2), \mathrm{B}(8…

If $\mathrm{P}(6,1)$ be the orthocentre of the triangle whose vertices are $\mathrm{A}(5,-2), \mathrm{B}(8,3)$ and $\mathrm{C}(\mathrm{h}, \mathrm{k})$, then the point $C$ lies on the circle:
  1. $x^2+y^2-61=0$
  2. $x^2+y^2-52=0$
  3. $x^2+y^2-65=0$
  4. $x^2+y^2-74=0$

Solution


Slope of $A D=3$ Slope of $\mathrm{BC}=-\frac{1}{3}$ equation of $\mathrm{BC}=3 \mathrm{y}+\mathrm{x}-17=0$ slope of $\mathrm{BE}=1$ Slope of $\mathrm{AC}=-1$ equation of $\mathrm{AC}$ is $\mathrm{x}+\mathrm{y}-3=0$ point $C$ is $(-4,7)$

Asked in: JEE Main 2024 (06 Apr Shift 2)

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