Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Show that if the curves ax 2 + by 2 = 1 and Ax 2 + By 2 = 1 are orthogonal then ab(A – B) = AB(a – b).
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
ax 2 + by 2 = 1 ⇒ 
= 
Ax 2 + By 2 = 1 ⇒ 
= 
Product of slopes = – 1
⇒ aAx 2 + bBy 2 = 0
Eliminating x 2 , y 2 . ⇒ 
= 0
⇒ (AbB – aAB) – (abB – abA) = 0
AB(b – a) – ab (B – A) = 0
⇒ ab(A – B) = AB(a – b)
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