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 orthocenter of the triangle PQR is:

y 2 = 2 x − 3 ……. (i)Equation of chord of contactPQ : r = O (y × 1) = (x + 0) – 3y = x – 3 ……… (ii)From (i) and (ii)y = 1 or 3 M P Q = 4 4 = 1 M Q R = 2 6 = 1 3 <!- [if gte mso 9]><xml> </xml><! [endif]-> M P Q × M P R = − 1 ⇒ P Q ⊥ P R <!- [if gte mso 9]><xml> </xml><! [endif]-> Orthocentre = P (2, -1)

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Conic Sections Ncert Solutions Maths class 11th Maths Class 11th

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 orthocenter of the triangle PQR is:

Option 1 -

(0, 1)

Option 2 -

(2, -1)

Option 3 -

(6, 3)

Option 4 -

(2, 1)

3 Views | Posted 2 months ago

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

$y^{2} = 2 x - 3$ ……. (i)

Equation of chord of contact

PQ : r = O

(y × 1) = (x + 0) – 3

y = x – 3 ……… (ii)

From (i) and (ii)

y = 1 or 3

$M P Q = \frac{4}{4} = 1$

$M Q R = \frac{2}{6} = \frac{1}{3}$

$M_{P Q} \times M_{P R} = - 1 \Rightarrow P Q ⊥ P R$

Orthocentre = P (2, -1)

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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 orthocenter of the triangle PQR is:

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