If the tangents drawn at the points P and Q on the parabola y2=2 x-3 intersect at the point R (0,1), then the orthocentre of the triangle PQR is :

Question

If the tangents drawn at the points P and Q on the parabola y2=2 x-3 intersect at the point R (0,1), then the orthocentre of the triangle PQR is : (A) (0,1) (B) (2,-1) (C) (6,3) (D) (2,1)

Tardigrade Admin · Accepted Answer

y2=2 x-3 ...(1) Equation of chord of contact PQ: r =0 yx 1=( x +0)-3 y=x-3...(2)

from (1) and (2) (x ⋅ 3)2=2 x-3 x2-8 x+12=0 (x-2)(x-6)=0 x=2 text or 6 y=-1 text or 3

MQR =(2/6)=(1/3) MPR =(2/6)=(1/3) MPR =(2/-2)=-1 MPQ × MPR =-⇒ PQ perp PR text Orthocentre = P (2,-1)

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

$(0, 1)$

$(2, - 1)$

$(6, 3)$

$(2, 1)$

Q. If the tangents drawn at the points P and Q on the parabola y2=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)

y2=2x−3 ...(1) Equation of chord of contact PQ:r=0 yx1=(x+0)−3 y=x−3...(2) from (1) and (2) (x⋅3)2=2x−3 x2−8x+12=0 (x−2)(x−6)=0 x=2 or 6 y=−1 or 3 MQR=62​=31​ MPR=62​=31​ MPR=−22​=−1 MPQ×MPR=−⇒PQ⊥PR Orthocentre =P(2,−1)

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

$(0, 1)$

$(2, - 1)$

$(6, 3)$

$(2, 1)$