If the tangents drawn at the points \[\mathrm{P}\] and \[\mathrm{Q}\] on the parabola y2=2x−3 intersect at the point R(0,1), then the orthocentre of the triangle PQR is :
Solutions · 1
Official solution
Equation of chord PQ
\[ \Rightarrow y \times 1 = x - 3\]
\[ \Rightarrow x - y = 3\]
For point P \& Q
Intersection of PQ with parabola \[P:(6,3)\,Q:(2, - 1)\]
Slope of RQ=−1 \& Slope of PQ=1
Therefore \[\angle PQR = 90^\circ \Rightarrow \] Orthocentre is at Q:(2,−1)