Application of DerivativeHard
Question
If a variable tangent to the curve x2y = c3 makes intercepts a, b on x and y axis respectively, then the value of a2b is -
Options
A.27c3
B.
c3
c3C.
c3
c3D.
c3
c3Solution
Let any point on the curve is 
y =
= - 2t3
Equation of tangent is
y - ct2 = 2t3
For x intercept
0 - ct2 = - 2t3
⇒ 
a =
For y intercept
b - ct2 = - 2t3
⇒ b - ct2 = 2t2c ⇒ b = 3ct2
Now a2b =
× 3ct2 = 
y =
= - 2t3Equation of tangent is
y - ct2 = 2t3
For x intercept
0 - ct2 = - 2t3
⇒ a =
For y intercept
b - ct2 = - 2t3
⇒ b - ct2 = 2t2c ⇒ b = 3ct2
Now a2b =
× 3ct2 = Create a free account to view solution
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