JEE Main 2022 · 28 Jul · Shift 1 · Mathematics Q11

MathematicsSingle correct+4 / -1Question 11 of 90

If the tangents drawn at the points P and Q on the parabola $y^2=2x-3$ intersect at the point R(0, 1), then the orthocentre of the triangle PQR is :

(0, 1)

(2, −1)

(6, 3)

(2, 1)

Answer and worked solution

Official answer: B

Chord of contact from (0, 1): $y=x-3$ . It meets the parabola where $x^2-8x+12=0$ : $P(2,-1)$ , $Q(6,3)$ .

Right angle at P. $\vec{PR}=(-2,2)$ and $\vec{PQ}=(4,4)$ are perpendicular, so the orthocentre is P.

(2, −1). (B)

JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 11