Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Show that the orthocentre of Δ formed by the straight lines, ax 2 + 2hxy + by 2 = 0 and x + my =1 is a point (x', y') such that 
= 
.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
ax 2 + 2hxy + by 2 ≡ b (y – m 1 n) (y – m 2 n)
m 1 + m 2 = 
, m 1 m 2 = 
The line x + my = 1 cuts y = m 1 x.
A 
Equation of line AD ⇒ y – 
= – 
x ( + mm 1 ) – 1 + m 2 {y ( + mm 1 ) – m 1 } = 0 ..........(1)
orthocentre also lies on mx – y = 0 or 
= 
= λ
put x = λ and y = m λ in (1)
∴ λ = 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The vertices of a triangle OBC are O(0,0) B(–3,–1) and C(–1,–3). Find the equation of line parallel…
A variable line, drawn through the point of intersection of the straight lines = 1 and = 1, meet…
From the vertices A, B, C of a triangle ABC, perpendiculars AD, BE, CF are drawn to any straight li…
A triangle is formed by the lines whose equations are AB : x + y – 5 = 0, BC : x + 7y – 7 = 0 and …
The coordinates of the feet of from the vertices of a Δ on the opposite sides are (20, 25), (8, 16…
Let P is any point inside the triangle ABC of side lengths 6, 5, 5 units and p 1 , p 2 , p 3 be the…