Coordinate Geometry
Straight Lines
MMTS_Full_Test_01
Grade 12
Question:
If $P(6,1)$ be the orthocentre of the triangle whose vertices are $A(5,-2)$, $B(8,3)$ and $C(h,k)$, then the point $C$ lies on the circle
$x^2+y^2-61=0$
$x^2+y^2-52=0$
$x^2+y^2-65=0$
$x^2+y^2-74=0$
Step-by-Step Solution
Key Concept: Use orthocenter condition: AP⊥BC and BP⊥AC
From AP⊥BC and BP⊥AC conditions: $h^2+k^2=74$. So $C$ lies on $x^2+y^2=74$.
Correct Answer: 4