Application of DerivativeMedium
Question
If the tangent at any point on the curve x4 + y4 = a4 cuts off intercept p and q on the axes, the value of p-4/3 + q-4/3 is-
Options
A.a-4/3
B.a-1/2
C.a1/2
D.None of these
Solution
x4 + y4 = a4
Let point is P(x1, y1)
4x3 + 4y3
= 0
x1 y1 = 
Intercept by it is p, q
y - y1 =
(x - x1)
y × y31 - y41 = - x x31 + x41
x x31 + y y31 = - x41 + y41
x x31 + y y31 = a4
p =
, q = 
p -4/3 + q -4/3 =
= a -16/3 (x41 + y41) = a -16/3 × a4
Let point is P(x1, y1)
4x3 + 4y3
= 0x1 y1 = Intercept by it is p, q
y - y1 =
(x - x1)y × y31 - y41 = - x x31 + x41
x x31 + y y31 = - x41 + y41
x x31 + y y31 = a4
p =
, q = p -4/3 + q -4/3 =
= a -16/3 (x41 + y41) = a -16/3 × a4
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