Application of DerivativeHard
Question
Which of the following pair(s) of curves is/are orthogonal.
Options
A.y2 = 4ax ; y = e-x/2a
B.y2 = 4ax; x2 = 4ay
C.xy = a2; x2 - y2 = b2
D.y = ax; x2 + y2 = c2
Solution
(a) 2y
= 4a ⇒ 
= m1
For IInd curve
= m2
m1m2 = - 1
(b) 2y
= 4a; 2x = 4a 
m1 =
m2 = 
y12 = 4ax1 ......(i)
= 4ay1 ...... (ii)
m1m2 ≠ - 1
(c) y =
; x2 - y2 = b2
m1 = -
; 2x1 - 2y1m2 = 0 ⇒ m2 = 
m1m2 =
= - 1
(d) m1 =
= a ; 2x + 2ym2 = 0
m2 = -
m1m2 =
= -1
= 4a ⇒ = m1For IInd curve
= m2m1m2 = - 1
(b) 2y
= 4a; 2x = 4a m1 =
m2 = y12 = 4ax1 ......(i)
= 4ay1 ...... (ii)m1m2 ≠ - 1
(c) y =
; x2 - y2 = b2m1 = -
; 2x1 - 2y1m2 = 0 ⇒ m2 = m1m2 =
= - 1(d) m1 =
= a ; 2x + 2ym2 = 0m2 = -
m1m2 =
= -1Create a free account to view solution
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