Coordinate Geometry
Parabola
MMTS_Full_Test_22
Grade 12
Question:
Let $\triangle PQR$ inscribed in parabola $y^2=4ax$ where $P=(at_1^2,2at_1)$, $Q=(at_2^2,2at_2)$, $R=(at_3^2,2at_3)$. The orthocentre of $\triangle PQR$ is
$(-a(t_1^2+t_2^2+t_3^2+t_1t_2+t_2t_3+t_3t_1),a(t_1+t_2+t_3+t_1t_2t_3))$
$(-a,a(t_1+t_2+t_3+t_1t_2t_3))$
$(-a,a(t_1+t_2+t_3-t_1t_2t_3))$
$(a(t_1+t_2+t_3),a)$
Step-by-Step Solution
Key Concept: Standard result for orthocentre of triangle on parabola
x-coordinate of orthocentre $=-a$ (standard result). y-coordinate $=a(t_1+t_2+t_3+t_1t_2t_3)$.
Correct Answer: 4