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
View Solution FreeMore Application of Derivative Questions
A curve with equation of the form y = ax4 + bx3 + cx + d has zero gradient at the point (0,1) and also touches the x-axi...The angle of intersection between the curvesy2 = 8x and x2 = 4y - 12 at (2, 4) is-...Consider the curve f(x) = x1/3, then -...At any point of a curve (subtangent) x (subnormal) is equal to the square of the-...The slopes of the tangents to the curve y = (x + 1) (x − 3) at the points where it crosses x- axis are -...